<?xml version="1.0" encoding="UTF-8"?>
<xml><records><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Radosław Adamczak</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Rafał Latała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Asymptotic entropic uncertainty relations</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2016</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">J. Math. Phys. </style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">57</style></VOLUME><SECTION><style face="normal" font="default" size="100%">032204</style></SECTION><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;Entropic uncertainty relations are analyzed for the case of N-dimensional Hilbert space and two orthogonal measurements performed in two generic bases, related by a Haar random unitary matrix U. We derive estimations for the average norms of truncations of U of a given size, which allow us to study state-independent lower bounds for the sum of two entropies describing the measurements outcomes. In particular, we show that the Maassen–Uffink bound asymptotically behaves as lnN−lnlnN−ln2, while the strong entropic majorization relation yields a nearly optimal bound, lnN−const. Analogous results are also obtained for a more general case of several orthogonal measurements performed in generic bases.&lt;/p&gt;&#13;
</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1412.7065v1</style></NOTES><URL><style face="normal" font="default" size="100%">http://dx.doi.org/10.1063/1.4944425</style></URL><title><style face="normal" font="default" size="100%">Asymptotic entropic uncertainty relations</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Charles Dunkl</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Piotr Gawron</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">J.A. Holbrook</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Jaroslaw Miszczak</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Numerical shadow and geometry of quantum states</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2011</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">J. Phys. A: Math. Theor.</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">44</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">33</style></NUMBER><PAGES><style face="normal" font="default" size="100%">335301</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">The totality of normalised density matrices of order N forms a convex set Q\_N in R^(N^2-1). Working with the flat geometry induced by the Hilbert-Schmidt distance we consider images of orthogonal projections of Q\_N onto a two-plane and show that they are similar to the numerical ranges of matrices of order N. For a matrix A of a order N one defines its numerical shadow as a probability distribution supported on its numerical range W(A), induced by the unitarily invariant Fubini-Study measure on the complex projective manifold CP^(N-1). We define generalized, mixed-states shadows of A and demonstrate their usefulness to analyse the structure of the set of quantum states and unitary dynamics therein.</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1104.2760 IF=1.641(2010);</style></NOTES><title><style face="normal" font="default" size="100%">Numerical shadow and geometry of quantum states</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Charles Dunkl</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Piotr Gawron</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">J.A. Holbrook</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Numerical shadows: measures and densities on the numerical range</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2011</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Linear Algebra Appl.</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">434</style></VOLUME><PAGES><style face="normal" font="default" size="100%">2042–2080</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">For any operator M acting on an N-dimensional Hilbert space H\_N we introduce its numerical shadow, which is a probability measure on the complex plane supported by the numerical range of M. The shadow of M at point z is defined as the probability that the inner product (Mu,u) is equal to z, where u stands for a random complex vector from H\_N, satisfying ||u||=1. In the case of N=2 the numerical shadow of a non-normal operator can be interpreted as a shadow of a hollow sphere projected on a plane. A similar interpretation is provided also for higher dimensions. For a hermitian M its numerical shadow forms a probability distribution on the real axis which is shown to be a one dimensional B-spline. In the case of a normal M the numerical shadow corresponds to a shadow of a transparent solid simplex in R^{N-1} onto the complex plane. Numerical shadow is found explicitly for Jordan matrices J\_N, direct sums of matrices and in all cases where the shadow is rotation invariant. Results concerning the moments of shadow measures play an important role. A general technique to study numerical shadow via the Cartesian decomposition is described, and a link of the numerical shadow of an operator to its higher-rank numerical range is emphasized.</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1010.4189 IF=1.005(2010);</style></NOTES><title><style face="normal" font="default" size="100%">Numerical shadows: measures and densities on the numerical range</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Charles Dunkl</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Piotr Gawron</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Real numerical shadow and generalized B-splines</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2015</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Linear Algebra and its Applications</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">479</style></VOLUME><PAGES><style face="normal" font="default" size="100%">12–51</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;arXiv:1409.4941&lt;/p&gt;&#13;
</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1409.4941</style></NOTES><URL><style face="normal" font="default" size="100%">https://doi.org/10.1016/j.laa.2015.03.029</style></URL><title><style face="normal" font="default" size="100%">Real numerical shadow and generalized B-splines</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">M. Enríquez</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Minimal Renyi-Ingarden-Urbanik entropy of multipartite quantum states</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2015</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Entropy</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">17</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">7</style></NUMBER><PAGES><style face="normal" font="default" size="100%">5063–5084</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;We study the entanglement of a pure state of a composite quantum system consisting of several subsystems with d levels each. It can be described by the R'enyi-Ingarden-Urbanik entropy Sq of a decomposition of the state in a product basis, minimized over all local unitary transformations. In the case q=0 this quantity becomes a function of the rank of the tensor representing the state, while in the limit q→∞ the entropy becomes related to the overlap with the closest separable state and the geometric measure of entanglement. For any bipartite system the entropy S1 coincides with the standard entanglement entropy. We analyze the distribution of the minimal entropy for random states of three and four-qubit systems. In the former case the distributions of 3-tangle is studied and some of its moments are evaluated, while in the latter case we analyze the distribution of the hyperdeterminant. The behavior of the maximum overlap of a three-qudit system with the closest separable state is also investigated in the asymptotic limit.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://doi.org/10.3390/e17075063</style></URL><title><style face="normal" font="default" size="100%">Minimal Renyi-Ingarden-Urbanik entropy of multipartite quantum states</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Bartłomiej Gardas</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Notes on the Riccati operator equation in open quantum systems</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2012</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">J. Math. Phys</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">53</style></VOLUME><PAGES><style face="normal" font="default" size="100%">012106</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;Recent problem [B. Gardas, J. Math. Phys. {bf 52}, 042104 (2011)] concerning an antilinear solution of the Riccati equation is solved. We also exemplify that a simplification of the Riccati equation, even under reasonable assumptions, can lead to a not equivalent equation.&lt;/p&gt;&#13;
</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1111.4380 IF=1.291(2010); 5IF=1.210(2010);</style></NOTES><title><style face="normal" font="default" size="100%">Notes on the Riccati operator equation in open quantum systems</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Bartłomiej Gardas</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Stationary states of two-level open quantum systems</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2011</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">J. Phys. A: Math. Theor.</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">44</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">21</style></NUMBER><PAGES><style face="normal" font="default" size="100%">215306</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;A problem of finding stationary states of open quantum systems is addressed. We focus our attention on a generic type of open system: a qubit coupled to its environment. We apply the theory of block operator matrices and find stationary states of two-level open quantum systems under certain conditions applied on both the qubit and the surrounding.&lt;/p&gt;&#13;
</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1006.3328 IF=1.641(2010);</style></NOTES><title><style face="normal" font="default" size="100%">Stationary states of two-level open quantum systems</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>7</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Piotr Gawron</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Przemysław Głomb</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Jaroslaw Miszczak</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Tadeusz Czachórski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Stanisław Kozielski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Urszula Stańczyk</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Eigengestures for natural human computer interface</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2011</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Man-Machine Interactions 2</style></SECONDARY_TITLE><PLACE_PUBLISHED><style face="normal" font="default" size="100%">Berlin / Heidelberg</style></PLACE_PUBLISHED><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><PUBLISHER><style face="normal" font="default" size="100%">Springer</style></PUBLISHER><PAGES><style face="normal" font="default" size="100%">49–56</style></PAGES><ISBN><style face="normal" font="default" size="100%">978-3-642-23168-1</style></ISBN><ABSTRACT><style face="normal" font="default" size="100%">We present the application of Principal Component Analysis for data acquired during the design of a natural gesture interface. We investigate the concept of an eigengesture for motion capture hand gesture data and present the visualisation of principal components obtained in the course of conducted experiments. We also show the influence of dimensionality reduction on reconstructed gesture data quality.</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1105.1293</style></NOTES><title><style face="normal" font="default" size="100%">Eigengestures for natural human computer interface</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Piotr Gawron</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Dariusz Kurzyk</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">A model for quantum queue</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2013</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">International Journal of Quantum Information</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">11</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">2</style></NUMBER><PAGES><style face="normal" font="default" size="100%">1350023</style></PAGES><NOTES><style face="normal" font="default" size="100%">arXiv:1210.8339</style></NOTES><title><style face="normal" font="default" size="100%">A model for quantum queue</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Piotr Gawron</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Jaroslaw Miszczak</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Ł. Skowronek</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Restricted numerical range: A versatile tool in the theory of quantum information</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2010</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">J. Math. Phys.</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">51</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">10</style></NUMBER><PAGES><style face="normal" font="default" size="100%">102204</style></PAGES><NOTES><style face="normal" font="default" size="100%">arXiv:0905.3646 IF=1.291(2010);</style></NOTES><title><style face="normal" font="default" size="100%">Restricted numerical range: A versatile tool in the theory of quantum information</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Przemysław Głomb</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Arkadiusz Sochan</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Context selection for efficient bit modeling of contourlet transform coefficients</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2007</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Theoretical and Applied Informatics</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">19</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">2</style></NUMBER><PAGES><style face="normal" font="default" size="100%">135–146</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">Contourlet transform is named as one possible successor to the wavelet transform as a tool for representation of image information. It has better properties in representation of edge information, which make it suitable for designing image compression systems. It is not clear, however, how to exploit the statistical structure of the coefficients generated by this transform in effective compression algorithm. In this work, authors propose a general, nonparametric method to achieve context map, thus allowing for efficient application of EBCOT/JPEG 2000 bit modeling and encoding approach to contourlet transformed images. The article presents the derivation of the method and experiments performed on a publicly available image set. Keywords: contourlet transform, coefficient bit modeling, context estimation</style></ABSTRACT><title><style face="normal" font="default" size="100%">Context selection for efficient bit modeling of contourlet transform coefficients</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">A. Lakshminarayan</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Diagonal unitary entangling gates and contradiagonal quantum states</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2014</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Phys. Rev. A</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">90</style></VOLUME><PAGES><style face="normal" font="default" size="100%">032303</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;Nonlocal properties of an ensemble of diagonal random unitary matrices of order N2 are investigated. The average Schmidt strength of such a bipartite diagonal quantum gate is shown to scale as logN, in contrast to the logN2 behavior characteristic to random unitary gates. Entangling power of a diagonal gate U is related to the von Neumann entropy of an auxiliary quantum state ρ=AA†/N2, where the square matrix A is obtained by reshaping the vector of diagonal elements of U of length N2 into a square matrix of order N. This fact provides a motivation to study the ensemble of non-hermitian unimodular matrices A, with all entries of the same modulus and random phases and the ensemble of quantum states ρ, such that all their diagonal entries are equal to 1/N. Such a state is contradiagonal with respect to the computational basis, in sense that among all unitary equivalent states it maximizes the entropy copied to the environment due to the coarse graining process. The first four moments of the squared singular values of the unimodular ensemble are derived, based on which we conjecture a connection to a recently studied combinatorial object called the&lt;/p&gt;&#13;
</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1407.1169 doi:10.1103/PhysRevA.90.032303</style></NOTES><URL><style face="normal" font="default" size="100%">https://doi.org/10.1103/PhysRevA.90.032303</style></URL><title><style face="normal" font="default" size="100%">Diagonal unitary entangling gates and contradiagonal quantum states</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">D. Markham</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Jaroslaw Miszczak</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Quantum state discrimination: A geometric approach</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2008</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Phys. Rev. A</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">77</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">4</style></NUMBER><PAGES><style face="normal" font="default" size="100%">042111</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">We analyze the problem of finding sets of quantum states that can be deterministically discriminated. From a geometric point of view, this problem is equivalent to that of embedding a simplex of points whose distances are maximal with respect to the Bures distance (or trace distance). We derive upper and lower bounds for the trace distance and for the fidelity between two quantum states, which imply bounds for the Bures distance between the unitary orbits of both states. We thus show that, when analyzing minimal and maximal distances between states of fixed spectra, it is sufficient to consider diagonal states only. Hence when optimal discrimination is considered, given freedom up to unitary orbits, it is sufficient to consider diagonal states. This is illustrated geometrically in terms of Weyl chambers.</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:0711.4286 IF=2.908(2008);</style></NOTES><title><style face="normal" font="default" size="100%">Quantum state discrimination: A geometric approach</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Jaroslaw Miszczak</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Piotr Gawron</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Qubit flip game on a Heisenberg spin chain</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2012</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Quantum Information Processing</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">11</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">6</style></NUMBER><PAGES><style face="normal" font="default" size="100%">1571–1583</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">We study a quantum version of a penny flip game played using control parameters of the Hamiltonian in the Heisenberg model. Moreover, we extend this game by introducing auxiliary spins which can be used to alter the behaviour of the system. We show that a player aware of the complex structure of the system used to implement the game can use this knowledge to gain higher mean payoff.</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1108.0642</style></NOTES><title><style face="normal" font="default" size="100%">Qubit flip game on a Heisenberg spin chain</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Jaroslaw Miszczak</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Paweł Horodecki</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">A. Uhlmann</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Sub- and super-fidelity as bounds for quantum fidelity</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2009</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%"/></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">9</style></VOLUME><NUMBER><style face="normal" font="default" size="100%"/></NUMBER><PAGES><style face="normal" font="default" size="100%">0103–0130</style></PAGES><DATE><style face="normal" font="default" size="100%">1</style></DATE><ABSTRACT><style face="normal" font="default" size="100%">We derive several bounds on fidelity between quantum states. In particular we show that fidelity is bounded from above by a simple to compute quantity we call super–fidelity. It is analogous to another quantity called sub–fidelity. For any two states of a two–dimensional quantum system ($N=2$) all three quantities coincide. We demonstrate that sub– and super–fidelity are concave functions. We also show that super–fidelity is super–multiplicative while sub–fidelity is sub–multiplicative and design feasible schemes to measure these quantities in an experiment. Super–fidelity can be used to define a distance between quantum states. With respect to this metric the set of quantum states forms a part of a $N^2-1$ dimensional hypersphere.</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:0805.2037 IF=2.980(209); IF5=2.402(2010);</style></NOTES><title><style face="normal" font="default" size="100%">Sub- and super-fidelity as bounds for quantum fidelity</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Piotr Gawron</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Jan Sładkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Enhancing pseudo-telepathy in the Magic Square game</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2013</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">PLOS ONE</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">8</style></VOLUME><PAGES><style face="normal" font="default" size="100%">e64694</style></PAGES><NOTES><style face="normal" font="default" size="100%">arXiv:1211.1213</style></NOTES><title><style face="normal" font="default" size="100%">Enhancing pseudo-telepathy in the Magic Square game</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Quantifying channels output similarity with applications to quantum control</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2016</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Quantum Information Processing</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">15</style></VOLUME><ISSUE><style face="normal" font="default" size="100%">4</style></ISSUE><SECTION><style face="normal" font="default" size="100%">1455</style></SECTION><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;In this work we aim at quantifying quantum channel output similarity. In order to achieve this, we introduce the notion of quantum channel superfidelity, which gives us an upper bound on the quantum channel fidelity. This quantity is expressed in a clear form using the Kraus representation of a quantum channel. As examples, we show potential applications of this quantity in the quantum control field.&lt;/p&gt;&#13;
</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1412.8694</style></NOTES><URL><style face="normal" font="default" size="100%">https://doi.org/10.1007/s11128-015-1238-z</style></URL><title><style face="normal" font="default" size="100%">Quantifying channels output similarity with applications to quantum control</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Quantum control robust with respect to coupling with an external environment</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2015</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Quantum Information Processing</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">14</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">2</style></NUMBER><PAGES><style face="normal" font="default" size="100%">437–446</style></PAGES><NOTES><style face="normal" font="default" size="100%">arXiv:1306.6826</style></NOTES><URL><style face="normal" font="default" size="100%">https://doi.org/10.1007/s11128-014-0879-7</style></URL><title><style face="normal" font="default" size="100%">Quantum control robust with respect to coupling with an external environment</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Quantum control with spectral constraints</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2014</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Quantum Information Processing.</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">13</style></VOLUME><PAGES><style face="normal" font="default" size="100%">227–237</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;Various constraints concerning control fields can be imposed in the realistic implementations of quantum control systems. One of the most important is the restriction on the frequency spectrum of acceptable control parameters. It is important to consider the limitations of experimental equipment when trying to find appropriate control parameters. Therefore, in this paper we present a general method of obtaining a piecewise-constant controls, which are robust with respect to spectral constraints. We consider here a Heisenberg spin chain, however the method can be applied to a system with more general interactions. To model experimental restrictions we apply an ideal low-pass filter to numerically obtained control pulses. The usage of the proposed method has negligible impact on the control quality as opposed to the standard approach, which does not take into account spectral limitations.&lt;/p&gt;&#13;
</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1204.6557</style></NOTES><URL><style face="normal" font="default" size="100%">https://doi.org/10.1007/s11128-013-0644-3</style></URL><title><style face="normal" font="default" size="100%">Quantum control with spectral constraints</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Local controllability of quantum systems</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2013</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Quantum Information Processing</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">12</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">1</style></NUMBER><PAGES><style face="normal" font="default" size="100%">459–466</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">We give a criterion that is sufficient for controllability of multipartite quantum systems. We generalize the graph infection criterion to the quantum systems that cannot be described with the use of a graph theory. We introduce the notation of hypergraphs and reformulate the infection property in this setting. The introduced criterion has a topological nature and therefore it is not connected to any particular experimental realization of quantum information processing.</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1203.4056</style></NOTES><title><style face="normal" font="default" size="100%">Local controllability of quantum systems</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Proof of Grabiner's theorem on non-colliding particles</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2005</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Probability and Mathematical Statistics</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">25</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">1</style></NUMBER><PAGES><style face="normal" font="default" size="100%">129–132</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">A detail proof of Grabiner's theorem [1] on the exact asymptotics of the time to collision for n independent Brownian motions is given.</style></ABSTRACT><title><style face="normal" font="default" size="100%">Proof of Grabiner's theorem on non-colliding particles</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Piotr Gawron</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Jaroslaw Miszczak</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Ł. Skowronek</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Man-Duen Choi</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Product numerical range in a space with tensor product structure</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2011</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Linear Algebra Appl.</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">434</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">1</style></NUMBER><PAGES><style face="normal" font="default" size="100%">327–342</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">We study operators acting on a tensor product Hilbert space and investigate their product numerical range, product numerical radius and separable numerical range. Concrete bounds for the product numerical range for Hermitian operators are derived. Product numerical range of a non-Hermitian operator forms a subset of the standard numerical range containing the barycenter of the spectrum. While the latter set is convex, the product range needs not to be convex nor simply connected. The product numerical range of a tensor product is equal to the Minkowski product of numerical ranges of individual factors.</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1008.3482 IF=1.005(2010);</style></NOTES><title><style face="normal" font="default" size="100%">Product numerical range in a space with tensor product structure</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">A. Jencova</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">M. Sedlak</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">M. Ziman</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Exploring boundaries of quantum convex structures: Special role of unitary processes</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2015</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Phys. Rev. A</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">92</style></VOLUME><PAGES><style face="normal" font="default" size="100%">012304</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;We address the question of finding the most effective convex decompositions into boundary elements (so-called boundariness) for sets of quantum states, observables and channels. First we show that in general convex sets the boundariness essentially coincides with the question of the most distinguishable element, thus, providing an operational meaning for this concept. Unexpectedly, we discovered that for any interior point of the set of channels the optimal decomposition necessarily contains a unitary channel. In other words, for any given channel the best distinguishable one is some unitary channel. Further, we prove that boundariness is sub-multiplicative under composition of systems and explicitly evaluate its maximal value that is attained only for the most mixed elements of the considered convex structures.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://doi.org/10.1103/PhysRevA.92.012304</style></URL><title><style face="normal" font="default" size="100%">Exploring boundaries of quantum convex structures: Special role of unitary processes</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Jaroslaw Miszczak</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Probability measure generated by the superfidelity</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2011</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">J. Phys. A: Math. Theor.</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">44</style></VOLUME><PAGES><style face="normal" font="default" size="100%">405301</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">We study the probability measure on the space of density matrices induced by the metric defined by using superfidelity. We give the formula for the probability density of eigenvalues. We also study some statistical properties of the set of density matrices equipped with the introduced measure and provide a method for generating density matrices according to the introduced measure.</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1107.2792 IF=1.641(2010);</style></NOTES><title><style face="normal" font="default" size="100%">Probability measure generated by the superfidelity</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Jaroslaw Miszczak</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Symbolic integration with respect to the Haar measure on the unitary groups</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2017</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Bulletin of the Polish Academy of Sciences Technical Sciences</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">65</style></VOLUME><ISSUE><style face="normal" font="default" size="100%">1</style></ISSUE><SECTION><style face="normal" font="default" size="100%">21</style></SECTION><DATE><style face="normal" font="default" size="100%">02/2017</style></DATE><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;We present IntU package for Mathematica computer algebra system. The presented package performs a symbolic integration of polynomial functions over the unitary group with respect to unique normalized Haar measure. We describe a number of special cases which can be used to optimize the calculation speed for some classes of integrals. We also provide some examples of usage of the presented package.&lt;/p&gt;&#13;
</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1109.4244</style></NOTES><URL><style face="normal" font="default" size="100%">https://doi.org/10.1515/bpasts-2017-0003</style></URL><title><style face="normal" font="default" size="100%">Symbolic integration with respect to the Haar measure on the unitary groups</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Jaroslaw Miszczak</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Bound on trace distance based on superfidelity</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2009</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Phys. Rev. A</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">79</style></VOLUME><PAGES><style face="normal" font="default" size="100%">024302</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">We provide a bound for the trace distance between two quantum states. The lower bound is based on the superfidelity, which provides the upper bound on quantum fidelity. One of the advantages of the presented bound is that it can be estimated using a simple measurement procedure. We also compare this bound with the one provided in terms of fidelity.</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:0811.2323 IF=2.866(2009);</style></NOTES><title><style face="normal" font="default" size="100%">Bound on trace distance based on superfidelity</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Jaroslaw Miszczak</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Piotr Gawron</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Charles Dunkl</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">J.A. Holbrook</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Restricted numerical shadow and geometry of quantum entanglement</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2012</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">J. Phys. A: Math. Theor.</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">45</style></VOLUME><PAGES><style face="normal" font="default" size="100%">415309</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">The restricted numerical range W\_R(A) of an operator A acting on a D-dimensional Hilbert space is defined as a set of all possible expectation values of this operator among pure states which belong to a certain subset R of the of set of pure quantum states of dimension D. One considers for instance the set of real states, or in the case of composite spaces, the set of product states and the set of maximally entangled states. Combining the operator theory with a probabilistic approach we introduce the restricted numerical shadow of A – a normalized probability distribution on the complex plane supported in W\_R(A). Its value at point z in C is equal to the probability that the expectation value is equal to z, where |psi&gt; represents a random quantum state in subset R distributed according to the natural measure on this set, induced by the unitarily invariant Fubini–Study measure. Studying restricted shadows of operators of a fixed size D=N\_A N\_B we analyse the geometry of sets of separable and maximally entangled states of the N\_A x N\_B composite quantum system. Investigating trajectories formed by evolving quantum states projected into the plane of the shadow we study the dynamics of quantum entanglement. A similar analysis extended for operators on D=2^3 dimensional Hilbert space allows us to investigate the structure of the orbits of GHZ and W quantum states of a three–qubit system.</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1201.2524</style></NOTES><title><style face="normal" font="default" size="100%">Restricted numerical shadow and geometry of quantum entanglement</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Jaroslaw Miszczak</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Piotr Gawron</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Bartłomiej Gardas</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Experimentally feasible measures of distance between quantum operations</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2011</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Quantum Information Processing</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">10</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">1</style></NUMBER><PAGES><style face="normal" font="default" size="100%">1–12</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;We present two measures of distance between quantum processes which can be measured directly in laboratory without resorting to process tomography. The measures are based on the superfidelity, introduced recently to provide an upper bound for quantum fidelity. We show that the introduced measures partially fulfill the requirements for distance measure between quantum processes. We also argue that they can be especially useful as diagnostic measures to get preliminary knowledge about imperfections in an experimental setup. In particular we provide quantum circuit which can be used to measure the superfidelity between quantum processes. We also provide a physical interpretation of the introduced metrics based on the continuity of channel capacity.&lt;/p&gt;&#13;
</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:0911.0567 IF=2.085(2010);</style></NOTES><title><style face="normal" font="default" size="100%">Experimentally feasible measures of distance between quantum operations</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Distinguishability of generic quantum states</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2016</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Physical Review A</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">93</style></VOLUME><ISSUE><style face="normal" font="default" size="100%">06</style></ISSUE><SECTION><style face="normal" font="default" size="100%">062112</style></SECTION><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;Properties of random mixed states of order N distributed uniformly with respect to the Hilbert-Schmidt measure are investigated. We show that for large N, due to the concentration of measure, the trace distance between two random states tends to a fixed number D&#160;=1/4+1/π, which yields the Helstrom bound on their distinguishability. To arrive at this result we apply free random calculus and derive the symmetrized Marchenko–Pastur distribution, which is shown to describe numerical data for the model of two coupled quantum kicked tops. Asymptotic values for the fidelity, Bures and transmission distances between two random states are obtained. Analogous results for quantum relative entropy and Chernoff quantity provide other bounds on the distinguishablity of both states in a multiple measurement setup due to the quantum Sanov theorem.&lt;/p&gt;&#13;
</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1507.05123</style></NOTES><URL><style face="normal" font="default" size="100%">https://doi.org/10.1103/PhysRevA.93.062112</style></URL><title><style face="normal" font="default" size="100%">Distinguishability of generic quantum states</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">T. Rolski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">The exact asymptotic of the collision time tail distribution for independent Brownian particles with different drifts</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2008</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Probability Theory and Related Fields</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">3-4</style></VOLUME><PAGES><style face="normal" font="default" size="100%">595–617</style></PAGES><DATE><style face="normal" font="default" size="100%">11</style></DATE><NOTES><style face="normal" font="default" size="100%">arXiv:0704.0215 IF=1.569(2008);</style></NOTES><title><style face="normal" font="default" size="100%">The exact asymptotic of the collision time tail distribution for independent Brownian particles with different drifts</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">T. Rolski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">The exact asymptotic of the time to collision</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2005</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Electronic Journal of Probability</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">10</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">40</style></NUMBER><PAGES><style face="normal" font="default" size="100%">1359–1380</style></PAGES><DATE><style face="normal" font="default" size="100%">11</style></DATE><ABSTRACT><style face="normal" font="default" size="100%">Abstract In this note we consider the time of the collision $tau$ for $n$ independent copies of Markov processes $X^1_t,. . .,X^n_t$, each starting from $x_i$,where $x_1 t) = t^{-n(n-1)/4}(Ch(x)+o(1)),$ where $C$ is known and $h(x)$ is the Vandermonde determinant. From the proof one can see that the result also holds for $X_t$ being the Brownian motion or the Poisson process. An application to skew standard Young tableaux is given.</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">IF=0.676(2006);</style></NOTES><title><style face="normal" font="default" size="100%">The exact asymptotic of the time to collision</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Ł. Rudnicki</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">K. Chabuda</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">M. Paraniak</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Certainty relations, mutual entanglement and non-displacable manifolds</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2015</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Phys. Rev. A</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">92</style></VOLUME><PAGES><style face="normal" font="default" size="100%">032109</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;{We derive explicit bounds for the average entropy characterizing measurements of a pure quantum state of size N in L orthogonal bases. Lower bounds lead to novel entropic uncertainty relations, while upper bounds allow us to formulate universal certainty relations. For L=2 the maximal average entropy saturates at logN as there exists a mutually coherent state, but certainty relations are shown to be nontrivial for L≥3 measurements. In the case of a prime power dimension&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://doi.org/10.1103/PhysRevA.92.032109</style></URL><title><style face="normal" font="default" size="100%">Certainty relations, mutual entanglement and non-displacable manifolds</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Ł. Rudnicki</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Majorization entropic uncertainty relations</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2013</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">J. Phys. A: Math. Theor.</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">46</style></VOLUME><PAGES><style face="normal" font="default" size="100%">272002</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">Entropic uncertainty relations in a finite dimensional Hilbert space are investigated. Making use of the majorization technique we derive explicit lower bounds for the sum of Renyi entropies describing probability distributions associated with a given pure state expanded in eigenbases of two observables. The bounds obtained are expressed in terms of the largest singular values of submatrices of the unitary rotation matrix. For a generic unitary matrix of size N = 5 the bound obtained is stronger than the one of Maassen and Uffink (MU) with probability larger than 98%, and this ratio increases with N. We show also that the bounds investigated are invariant for unitary matrices equivalent up to dephasing and permutation and derive a classical analogue of the MU uncertainty relation formulated for stochastic transition matrices.</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1304.7755</style></NOTES><title><style face="normal" font="default" size="100%">Majorization entropic uncertainty relations</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Wojciech Roga</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Ł. Rudnicki</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Entropic trade-off relations for quantum operations</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2013</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Phys. Rev. A</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">87</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">3</style></NUMBER><PAGES><style face="normal" font="default" size="100%">032308</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">Spectral properties of an arbitrary matrix can be characterized by the entropy of its rescaled singular values. Any quantum operation can be described by the associated dynamical matrix or by the corresponding superoperator. The entropy of the dynamical matrix describes the degree of decoherence introduced by the map, while the entropy of the superoperator characterizes the a priori knowledge of the receiver of the outcome of a quantum channel Φ. We prove that for any map acting on an N-dimensional quantum system the sum of both entropies is not smaller than lnN. For any bistochastic map this lower bound reads 2lnN. We investigate also the corresponding Rényi entropies, providing an upper bound for their sum, and analyze the entanglement of the bi-partite quantum state associated with the channel.</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1206.2536 doi: 10.1103/PhysRevA.87.032308</style></NOTES><title><style face="normal" font="default" size="100%">Entropic trade-off relations for quantum operations</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Ł. Rudnicki</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Paweł Horodecki</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Constructive entanglement test from triangle inequality</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2014</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">J. Phys. A: Math. Theor.</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">47</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">42</style></NUMBER><PAGES><style face="normal" font="default" size="100%">424035</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;We derive a simple lower bound on the geometric measure of entanglement for mixed quantum states in the case of a general multipartite system. The main ingredient of the presented derivation is the triangle inequality applied to the root infidelity distance in the space of density matrices. The obtained bound leads to entanglement criteria with a straightforward interpretation. The proposed criteria provide an experimentally accessible, powerful entanglement test. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.&lt;/p&gt;&#13;
</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1211.2306</style></NOTES><URL><style face="normal" font="default" size="100%">https://doi.org/10.1088/1751-8113/47/42/424035</style></URL><title><style face="normal" font="default" size="100%">Constructive entanglement test from triangle inequality</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Ł. Rudnicki</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Paweł Horodecki</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Collectibility for Mixed Quantum States</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2012</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Phys. Rev. A</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">86</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">6</style></NUMBER><PAGES><style face="normal" font="default" size="100%">062329</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for pure states only [ Phys. Rev. Lett. 107 150502 (2011)], is extended here for mixed quantum states. We define collectibility for any mixed states of a multipartite system. Deriving bounds for collectibility for positive partially transposed states of given purity provides insight into the structure of entangled quantum states. In the case of two qubits the application of complementary measurements and coincidence based detections leads to a test of entanglement of pseudopure states.</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1211.0573 doi:10.1103/PhysRevA.86.062329</style></NOTES><title><style face="normal" font="default" size="100%">Collectibility for Mixed Quantum States</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Ł. Rudnicki</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Strong Majorization Entropic Uncertainty Relations</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2014</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Phys. Rev. A</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">89</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">5</style></NUMBER><PAGES><style face="normal" font="default" size="100%">052115</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;We analyze entropic uncertainty relations in a finite dimensional Hilbert space and derive several strong bounds for the sum of two entropies obtained in projective measurements with respect to any two orthogonal bases. We improve the recent bounds by Coles and Piani [ArXiv:1307.4265], which are known to be stronger than the well known result of Maassen and Uffink. Furthermore, we find a novel bound based on majorization techniques, which also happens to be stronger than the recent results involving largest singular values of submatrices of the unitary matrix connecting both bases. The firsts set of new bounds give better results for unitary matrices close to the Fourier matrix, while the second one works better in the opposite sectors. Some results derived admit generalization to arbitrary mixed states and the bounds are increased by the von Neumann entropy of the measured state&lt;/p&gt;&#13;
</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1402.0129</style></NOTES><URL><style face="normal" font="default" size="100%">https://doi.org/10.1103/PhysRevA.89.052115</style></URL><title><style face="normal" font="default" size="100%">Strong Majorization Entropic Uncertainty Relations</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Ryszard Winiarczyk</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Piotr Gawron</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Jaroslaw Miszczak</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Analysis of patent activity in the field of quantum information processing</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2013</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">International Journal of Quantum Information</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">11</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">1</style></NUMBER><PAGES><style face="normal" font="default" size="100%">1350007</style></PAGES><NOTES><style face="normal" font="default" size="100%">arXiv:1212.2439</style></NOTES><title><style face="normal" font="default" size="100%">Analysis of patent activity in the field of quantum information processing</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">P. Zawadzki</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Jaroslaw Miszczak</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Increasing the security of the ping-pong protocol by using many mutually unbiased bases</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2013</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Quantum Information Processing</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">12</style></VOLUME><NUMBER><style face="normal" font="default" size="100%">1</style></NUMBER><PAGES><style face="normal" font="default" size="100%">569–576</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">In this paper we propose an extended version of the ping-pong protocol and study its security. The proposed protocol incorporates the usage of mutually unbiased bases in the control mode. We show that, by increasing the number of bases, it is possible to improve the security of this protocol. We also provide the upper bounds on eavesdropping average non-detection probability and propose a control mode modification that increases the attack detection probability.</style></ABSTRACT><NOTES><style face="normal" font="default" size="100%">arXiv:1201.3230</style></NOTES><title><style face="normal" font="default" size="100%">Increasing the security of the ping-pong protocol by using many mutually unbiased bases</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Piotr Gawron</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Jacek Szklarski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Wybory samorządowe 2014 w poszukiwaniu anomalii statystycznych</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2015</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Electoral Studies</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">30</style></VOLUME><PAGES><style face="normal" font="default" size="100%">534–545</style></PAGES><title><style face="normal" font="default" size="100%">Wybory samorządowe 2014 w poszukiwaniu anomalii statystycznych</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Ion Nechita</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Almost all quantum channels are equidistant</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2018</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Journal of Mathematical Physics</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">59</style></VOLUME><PAGES><style face="normal" font="default" size="100%">052201</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;In this work we analyze properties of generic quantum channels in the case of large system size. We use the random matrix theory and free probability to show that the distance between two independent random channels tends to a constant value as the dimension of the system grows larger. As a measure of the distance we use the diamond norm. In the case of a flat Hilbert-Schmidt distribution on quantum channels, we obtain that the distance converges to &lt;span style="font-size:129%"&gt;1/2&lt;em&gt;+2/π&lt;/em&gt;&lt;/span&gt;. Furthermore, we show that for a random state &lt;span style="font-size:129%"&gt;&lt;em&gt;ρ&lt;/em&gt;&lt;/span&gt; acting on a bipartite Hilbert space $H_A \otimes H_B$, sampled from the Hilbert-Schmidt distribution, the reduced states $Tr_A\rho$ and $Tr_B \rho$ are arbitrarily close to the maximally mixed state. This implies that, for large dimensions, the state &lt;span style="font-size:129%"&gt;&lt;em&gt;ρ&lt;/em&gt;&lt;/span&gt; may be interpreted as a Jamio{\l}kowski state of a unital map.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://doi.org/10.1063/1.5019322</style></URL><title><style face="normal" font="default" size="100%">Almost all quantum channels are equidistant</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Marcin Markiewicz</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Anna de Rosier</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Wiesław Laskowski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Quantum noise generated by local random Hamiltonians</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2017</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Physical Review A</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">95</style></VOLUME><SECTION><style face="normal" font="default" size="100%">032333</style></SECTION><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;We investigate the impact of a local random unitary noise on multipartite quantum states of arbitrary dimension. We follow the dynamical approach, in which the single-particle unitaries are generated by local random Hamiltonians. Assuming short evolution time we derive an upper bound on the fidelity between an initial and the final state transformed by this type of noise. This result is based on averaging the Tamm-Mandelstam bound and holds for a wide class of distributions of random Hamiltonians fulfilling specific symmetry conditions. It is showed that the sensitivity of a given pure quantum state to the discussed type of noise depends only on the properties of a single-particle and bipartite reduced states.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://doi.org/10.1103/PhysRevA.95.032333</style></URL><title><style face="normal" font="default" size="100%">Quantum noise generated by local random Hamiltonians</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Łukasz Rudnicki</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Gauge invariant information concerning quantum channels</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2018</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Quantum</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">2</style></VOLUME><PAGES><style face="normal" font="default" size="100%">60</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;Motivated by the gate set tomography we study quantum channels from the perspective of information which is invariant with respect to the gauge realized through similarity of matrices representing channel superoperators. We thus use the complex spectrum of the superoperator to provide necessary conditions relevant for complete positivity of qubit channels and to express various metrics such as average gate fidelity.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://doi.org/10.22331/q-2018-04-11-60</style></URL><title><style face="normal" font="default" size="100%">Gauge invariant information concerning quantum channels</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Dariusz Kurzyk</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Conditional entropic uncertainty relations for Tsallis entropies</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2018</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Quantum Information Processing</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">17</style></VOLUME><PAGES><style face="normal" font="default" size="100%">193</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;The entropic uncertainty relations are a very active field of scientific inquiry. Their applications include quantum cryptography and studies of quantum phenomena such as correlations and non-locality. In this work we find state-independent entropic uncertainty relations in terms of the Tsallis entropies for states with a fixed amount of entanglement. Our main result is stated as Theorem. Taking the special case of von Neumann entropy and utilizing the concavity of conditional von Neumann entropies, we extend our result to mixed states. Finally we provide a lower bound on the amount of extractable key in a quantum cryptographic scenario.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://doi.org/10.1007/s11128-018-1955-1</style></URL><title><style face="normal" font="default" size="100%">Conditional entropic uncertainty relations for Tsallis entropies</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Adam Glos</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Aleksandra Krawiec</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Ryszard Kukulski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Vertices cannot be hidden from quantum spatial search for almost all random graphs</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2018</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Quantum Information Processing</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">17</style></VOLUME><PAGES><style face="normal" font="default" size="100%">81</style></PAGES><URL><style face="normal" font="default" size="100%">https://doi.org/10.1007/s11128-018-1844-7</style></URL><title><style face="normal" font="default" size="100%">Vertices cannot be hidden from quantum spatial search for almost all random graphs</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Rudnicki</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Aleksandra Krawiec</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Majorization uncertainty relations for mixed quantum states</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2018</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Journal of Physics A: Mathematical and Theoretical</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">51</style></VOLUME><ISSUE><style face="normal" font="default" size="100%">17</style></ISSUE><SECTION><style face="normal" font="default" size="100%">175306</style></SECTION><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;Majorization uncertainty relations are generalized for an arbitrary mixed quantum state &lt;span style="font-size:129%"&gt;&lt;em&gt;ρ&lt;/em&gt;&lt;/span&gt; of a finite size &lt;span style="font-size:129%"&gt;&lt;em&gt;N&lt;/em&gt;&lt;/span&gt;. In particular, a lower bound for the sum of two entropies characterizing probability distributions corresponding to measurements with respect to arbitrary two orthogonal bases is derived in terms of the spectrum of &lt;span style="font-size:129%"&gt;&lt;em&gt;ρ&lt;/em&gt;&lt;/span&gt; and the entries of a unitary matrix &lt;span style="font-size:129%"&gt;&lt;em&gt;U&lt;/em&gt;&lt;/span&gt; relating both bases. The obtained results can also be formulated for two measurements performed on a single subsystem of a bipartite system described by a pure state, and consequently expressed as uncertainty relation for the sum of conditional entropies.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://doi.org/10.1088/1751-8121/aab66c</style></URL><title><style face="normal" font="default" size="100%">Majorization uncertainty relations for mixed quantum states</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Kamil Korzekwa</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Stanisław Czachórski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Coherifying quantum channels</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2018</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">New Journal of Physics</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">20</style></VOLUME><PAGES><style face="normal" font="default" size="100%">043028</style></PAGES><DATE><style face="normal" font="default" size="100%">04/2018</style></DATE><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;Is it always possible to explain random stochastic transitions between states of a finite-dimensional system as arising from the deterministic quantum evolution of the system? If not, then what is the minimal amount of randomness required by quantum theory to explain a given stochastic process? Here, we address this problem by studying possible coherifications of a quantum channel $\Phi$, i.e., we look for channels $\Phi^{\mathcal{C}}$ that induce the same classical transitions $T$, but are "more coherent". To quantify the coherence of a channel $\Phi$ we measure the coherence of the corresponding Jamio{\l}kowski state $J_{\Phi}$. We show that the classical transition matrix $T$ can be coherified to reversible unitary dynamics if and only if $T$ is unistochastic. Otherwise the Jamio{\l}kowski state $J_\Phi^{\mathcal{C}}$ of the optimally coherified channel is mixed, and the dynamics must necessarily be irreversible. To asses the extent to which an optimal process $\Phi^{\mathcal{C}}$ is indeterministic we find explicit bounds on the entropy and purity of $J_\Phi^{\mathcal{C}}$, and relate the latter to the unitarity of $\Phi^{\mathcal{C}}$. We also find optimal coherifications for several classes of channels, including all one-qubit channels. Finally, we provide a non-optimal coherification procedure that works for an arbitrary channel $\Phi$ and reduces its rank (the minimal number of required Kraus operators) from $d^2$ to $d$.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://doi.org/10.1088/1367-2630/aaaff3</style></URL><title><style face="normal" font="default" size="100%">Coherifying quantum channels</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Marcin Markiewicz</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Adrian Kolodziejski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Adam Rutkowski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Tomasz Tylec</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Wieslaw Laskowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Unified approach to geometric and positive-map-based non-linear entanglement identifiers</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2018</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Phys. Rev. A </style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">97</style></VOLUME><PAGES><style face="normal" font="default" size="100%">042339</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;Detecting quantumness of correlations (especially entanglement) is a very hard task even in the simplest case, i.e., two-partite quantum systems. Here we provide an analysis of whether there exists a relation between two of the most popular types of entanglement identifiers: the first one based on positive maps and not directly applicable in the laboratory and the second one a geometric entanglement identifier which is based on specific Hermiticity-preserving maps. We show a profound relation between those two types of entanglement criteria. Hereunder we have proposed a general framework of nonlinear functional entanglement identifiers which allows us to construct experimentally friendly entanglement criteria.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://doi.org/10.1103/PhysRevA.97.042339</style></URL><title><style face="normal" font="default" size="100%">Unified approach to geometric and positive-map-based non-linear entanglement identifiers</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Dariusz Kurzyk</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Unconditional Security of a K-State Quantum Key Distribution Protocol</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2018</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Quantum Information Processing</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">17</style></VOLUME><PAGES><style face="normal" font="default" size="100%">228</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;Quantum key distribution protocols constitute an important part of quantum cryptography, where the security of sensitive information arises from the laws of physics. In this paper we introduce a new family of key distribution protocols and we compare its key with the well-known protocols such as BB84, PBC0 and generation rate to the well-known protocols such as BB84, PBC0 and R04. We also state the security analysis of these protocols based on the entanglement distillation and CSS codes techniques.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://doi.org/10.1007/s11128-018-1998-3</style></URL><title><style face="normal" font="default" size="100%">Unconditional Security of a K-State Quantum Key Distribution Protocol</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Aleksandra Krawiec</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Ryszard Kukulski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Strategies for optimal single-shot discrimination of quantum measurements</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2018</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Physical Review A</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">98</style></VOLUME><ISSUE><style face="normal" font="default" size="100%">4</style></ISSUE><SECTION><style face="normal" font="default" size="100%">042103</style></SECTION><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;In this work we study the problem of single-shot discrimination of von Neumann measurements. We associate each measurement with a measure-and-prepare channel. There are two possible approaches to this problem. The first one, which is simple, does not utilize entanglement. We focus only on discrimination of classical probability distribution, which are outputs of the channels. We find necessary and sufficient criterion for perfect discrimination in this case. A more advanced approach requires the usage and entanglement. We quantify the distance of the two measurements in terms of the diamond norm (called sometimes the completely bounded trace norm). We provide an exact expression for the optimal probability of correct distinction and relate it to the discrimination of unitary channels. We also state a necessary and sufficient condition for perfect discrimination and a semidefinite program which checks this condition. Our main result, however, is a cone program which calculates the distance of these measurements and hence provides an upper bound on the probability of their correct distinction. As a by-product the program also finds a strategy (input state) which achieves this bound. Finally, we provide a full description for the cases of Fourier matrices and mirror isometries.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://arxiv.org/abs/1804.05856</style></URL><title><style face="normal" font="default" size="100%">Strategies for optimal single-shot discrimination of quantum measurements</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Michał Oszmaniec</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Filip Maciejewski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Simulating all quantum measurements using only projective measurements and postselection</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2019</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Physical Review A</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">100</style></VOLUME><PAGES><style face="normal" font="default" size="100%">012351</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;Implementation of generalized quantum measurements is often experimentally demanding, as it requires performing a projective measurement on a system of interest extended by the ancilla. We report an alternative scheme for implementing generalized measurements that uses solely: (a) classical randomness and post-processing, (b) projective measurements on a relevant quantum system and (c) postselection on non-observing certain outcomes. The method implements arbitrary quantum measurement in d dimensional system with success probability 1/d. It is optimal in the sense that for any dimensionn d there exist measurements for which the success probability cannot be higher. We apply our results to bound the relative power of projective and generalised measurements for unambiguous state discrimination. Finally, we test our scheme experimentally on IBM quantum processor. Interestingly, due to noise involved in the implementation of entangling gates, the quality with which our scheme implements generalized qubit measurements is higher than the one obtained with the standard construction using the auxiliary system.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://arxiv.org/abs/1807.08449v1</style></URL><title><style face="normal" font="default" size="100%">Simulating all quantum measurements using only projective measurements and postselection</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Aleksandra Krawiec</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Ryszard Kukulski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Michał Oszmaniec</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Multiple-shot and unambiguous discrimination of von Neumann measurements</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2021</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Quantum</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">5</style></VOLUME><SECTION><style face="normal" font="default" size="100%">425</style></SECTION><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;We present an in-depth study of the problem of discrimination of von Neumann measurements in finite-dimensional Hilbert spaces. Specifically, we consider two scenarios: unambiguous and multiple-shot discrimination. In the first scenario we give the general expressions for the optimal discrimination probabilities with and without the assistance of entanglement. In the case of multiple-shot discrimination, we focus on discrimination of measurements with the assistance of entanglement. Interestingly, we prove that in this setting all pairs of distinct von Neumann measurements can be distinguished perfectly (i.e. with the unit success probability) using only a finite number of queries. We also show that in this scenario queering the measurements \emph{in parallel} gives the optimal strategy and hence any possible adaptive methods do not offer any advantage over the parallel scheme. Finally, we show that typical pairs of Haar-random von Neumann measurements can be perfectly distinguished with only two queries.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://quantum-journal.org/papers/q-2021-04-06-425/pdf/</style></URL><title><style face="normal" font="default" size="100%">Multiple-shot and unambiguous discrimination of von Neumann measurements</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Kamil Korzekwa</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Stanisław Czachórski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Distinguishing classically indistinguishable states and channels</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2019</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%"> Journal of Physics A: Mathematical and Theoretical</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">52</style></VOLUME><PAGES><style face="normal" font="default" size="100%">475303</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;We investigate an original family of quantum distinguishability problems, where the goal is to perfectly distinguish between &lt;span style="font-size:129%"&gt;&lt;em&gt;M&lt;/em&gt;&lt;/span&gt; quantum states that become identical under a completely decohering map. Similarly, we study distinguishability of &lt;span style="font-size:129%"&gt;&lt;em&gt;M&lt;/em&gt;&lt;/span&gt; quantum channels that cannot be distinguished when one is restricted to decohered input and output states. The studied problems arise naturally in the presence of a superselection rule, allow one to quantify the amount of information that can be encoded in phase degrees of freedom (coherences), and are related to time-energy uncertainty relation. We present a collection of results on both necessary and sufficient conditions for the existence of &lt;span style="font-size:129%"&gt;&lt;em&gt;M&lt;/em&gt;&lt;/span&gt; perfectly distinguishable states (channels) that are classically indistinguishable.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://arxiv.org/abs/1812.09083</style></URL><title><style face="normal" font="default" size="100%">Distinguishing classically indistinguishable states and channels</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Rudnicki</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Pauli semigroups and unistochastic quantum channels</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2019</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Physics Letters A</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">383</style></VOLUME><ISSUE><style face="normal" font="default" size="100%">20</style></ISSUE><PAGES><style face="normal" font="default" size="100%">2376-2381</style></PAGES><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;We adopt the perspective of similarity equivalence, in gate set tomography called the gauge, to analyze various properties of quantum operations belonging to a semigroup, &lt;span style="font-size:122%"&gt;&lt;span style="font-family:stixgeneral"&gt;Φ&lt;/span&gt;&lt;span style="font-family:stixgeneral"&gt;=&lt;/span&gt;&lt;em&gt;e&lt;/em&gt;&lt;em&gt;^{Lt}&lt;/em&gt;&lt;/span&gt;,and therefore given through the Lindblad operator. We first observe that the non unital part of the channel decouples from the time evolution. Focusing on unital operations we restrict our attention to the single-qubit case, showing that the semigroup embedded inside the tetrahedron of Pauli channels is bounded by the surface composed of product probability vectors and includes the identity map together with the maximally depolarizing channel. Consequently, every member of the Pauli semigroup is unitarily equivalent to a unistochastic map, describing a coupling with one-qubit environment initially in the maximally mixed state, determined by a unitary matrix of order four.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://arxiv.org/abs/1903.12448</style></URL><title><style face="normal" font="default" size="100%">Pauli semigroups and unistochastic quantum channels</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Kamil Korzekwa</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Marco Tomamichel</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Encoding classical information into quantum resources</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2022</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">IEEE Transactions on Information Theory</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">68</style></VOLUME><ISSUE><style face="normal" font="default" size="100%">7</style></ISSUE><SECTION><style face="normal" font="default" size="100%">4518 - 4530</style></SECTION><DATE><style face="normal" font="default" size="100%">03/2022 </style></DATE><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;We introduce and analyse the problem of encoding classical information into different resources of a quantum state. More precisely, we consider a general class of communication scenarios characterised by encoding operations that commute with a unique resource destroying map and leave free states invariant. Our motivating example is given by encoding information into coherences of a quantum system with respect to a fixed basis (with unitaries diagonal in that basis as encodings and the decoherence channel as a resource destroying map), but the generality of the framework allows us to explore applications ranging from super-dense coding to thermodynamics. For any state, we find that the number of messages that can be encoded into it using such operations in a one-shot scenario is upper-bounded in terms of the information spectrum relative entropy between the given state and its version with erased resources. Furthermore, if the resource destroying map is a twirling channel over some unitary group, we find matching one-shot lower-bounds as well. In the asymptotic setting where we encode into many copies of the resource state, our bounds yield an operational interpretation of resource monotones such as the relative entropy of coherence and its corresponding relative entropy variance.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://dx.doi.org/10.1109/TIT.2022.3157440</style></URL><title><style face="normal" font="default" size="100%">Encoding classical information into quantum resources</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Aleksandra Krawiec</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Discrimination of POVMs with rank-one effects</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2020</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Quantum Information Processing</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">19</style></VOLUME><SECTION><style face="normal" font="default" size="100%">428</style></SECTION><title><style face="normal" font="default" size="100%">Discrimination of POVMs with rank-one effects</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Fereshte Shahbeigi</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">David Amaro-Alcalá</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Log-Convex set of Lindblad semigroups acting on N -level system</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2021</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Journal of Mathematical Physics</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">62</style></VOLUME><SECTION><style face="normal" font="default" size="100%">072105</style></SECTION><DATE><style face="normal" font="default" size="100%">07/2021</style></DATE><URL><style face="normal" font="default" size="100%">https://doi.org/10.1063/5.0009745</style></URL><title><style face="normal" font="default" size="100%">Log-Convex set of Lindblad semigroups acting on N -level system</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Paulina Lewandowska</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Aleksandra Krawiec</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Ryszard Kukulski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">On the optimal certification of von Neumann measurements</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2021</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Scientific Reports</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">11</style></VOLUME><ISSUE><style face="normal" font="default" size="100%">1</style></ISSUE><SECTION><style face="normal" font="default" size="100%">1-16</style></SECTION><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;Certification and validation of sources producing quantum states and measurement devices are a necessary step of quantum technology. Certification of quantum measurements is entwined with quantum hypotheses testing, however, we are allowed to prepare an input state and the final measurement. In this report, we begin with studying the two-point certification of pure quantum states and unitary channels to later use them to prove our main result, which is the certification of von Neumann measurements in single-shot and parallel scenarios. In particular, in all the above-mentioned scenarios we characterize the optimal probability of the type II error given some fixed statistical significance. We also state the conditions when two quantum objects cannot be distinguished perfectly but still can be certified. Moreover, we show the connection between the certification of quantum channels and the notion of&#160;q-numerical range.&lt;/p&gt;&#13;
</style></ABSTRACT><title><style face="normal" font="default" size="100%">On the optimal certification of von Neumann measurements</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Ryszard Kukulski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Ion Nechita</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Generating random quantum channels</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2021</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Journal of Mathematical Physics</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">62</style></VOLUME><SECTION><style face="normal" font="default" size="100%">062201</style></SECTION><DATE><style face="normal" font="default" size="100%">07/2021</style></DATE><URL><style face="normal" font="default" size="100%">https://doi.org/10.1063/5.0038838</style></URL><title><style face="normal" font="default" size="100%">Generating random quantum channels</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Grzegorz Rajchel-Mieldzioć</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Kamil Korzekwa</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Algebraic and geometric structures inside the Birkhoff polytope</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2022</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Journal of Mathematical Physics</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">63</style></VOLUME><SECTION><style face="normal" font="default" size="100%">012202</style></SECTION><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;The Birkhoff polytope Bd consisting of all bistochastic matrices of order d assists researchers from many areas, including combinatorics, statistical physics and quantum information. Its subset Ud of unistochastic matrices, determined by squared moduli of unitary matrices, is of a particular importance for quantum theory as classical dynamical systems described by unistochastic transition matrices can be quantised. In order to investigate the problem of unistochasticity we introduce the set Ld of bracelet matrices that forms a subset of Bd , but a superset of Ud . We prove that for every dimension d this set contains the set of factorisable bistochastic matrices Fd and is closed under matrix multiplication by elements of Fd. Moreover, we prove that both Ld and Fd are star-shaped with respect to the flat matrix. We also analyse the set of d × d unistochastic matrices arising from circulant unitary matrices, and show that their spectra lie inside d-hypocycloids on the complex plane. Finally, applying our results to small dimensions, we fully characterise the set of circulant unistochastic matrices of order d ≤ 4, and prove that such matrices form a monoid for d = 3.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://doi.org/10.1063/5.0046581</style></URL><title><style face="normal" font="default" size="100%">Algebraic and geometric structures inside the Birkhoff polytope</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Aleksandra Krawiec</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Excluding false negative error in certification of quantum channels</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2021</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Scientific Reports</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">11</style></VOLUME><ISSUE><style face="normal" font="default" size="100%">1</style></ISSUE><SECTION><style face="normal" font="default" size="100%">21716 </style></SECTION><DATE><style face="normal" font="default" size="100%">11/2021</style></DATE><URL><style face="normal" font="default" size="100%">https://www.nature.com/articles/s41598-021-00444-x.pdf</style></URL><title><style face="normal" font="default" size="100%">Excluding false negative error in certification of quantum channels</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Dariusz Kurzyk</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Relating entropies of quantum channels</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2021</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Entropy</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">23</style></VOLUME><ISSUE><style face="normal" font="default" size="100%">8</style></ISSUE><SECTION><style face="normal" font="default" size="100%">1028</style></SECTION><title><style face="normal" font="default" size="100%">Relating entropies of quantum channels</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Kamil Korzekwa</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Roberto Salazar</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Paweł Horodecki</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Dephasing superchannels</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2021</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Physical Review A</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">104</style></VOLUME><SECTION><style face="normal" font="default" size="100%">052611</style></SECTION><DATE><style face="normal" font="default" size="100%">11/2021</style></DATE><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;We characterise a class of environmental noises that decrease coherent properties of quantum channels by introducing and analysing the properties of dephasing superchannels. These are defined as superchannels that affect only non-classical properties of a quantum channel &lt;em&gt;E&lt;/em&gt;, i.e., they leave invariant the transition probabilities induced by &lt;em&gt;E&lt;/em&gt; in the distinguished basis. We prove that such superchannels ΞC form a particular subclass of Schur-product supermaps that act on the Jamiolkowski state J(&lt;em&gt;E&lt;/em&gt;) of a channel &lt;em&gt;E&lt;/em&gt; via a Schur product, J′=J∘C. We also find physical realizations of general ΞC through a pre- and post-processing employing dephasing channels with memory, and show that memory plays a non-trivial role for quantum systems of dimension d&gt;2. Moreover, we prove that coherence generating power of a general quantum channel is a monotone under dephasing superchannels. Finally, we analyse the effect dephasing noise can have on a quantum channel &lt;em&gt;E&lt;/em&gt; by investigating the number of distinguishable channels that &lt;em&gt;E&lt;/em&gt; can be mapped to by a family of dephasing superchannels. More precisely, we upper bound this number in terms of hypothesis testing channel divergence between &lt;em&gt;E&lt;/em&gt; and its fully dephased version, and also relate it to the robustness of coherence of &lt;em&gt;E&lt;/em&gt;.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://doi.org/10.1103/PhysRevA.104.052611</style></URL><title><style face="normal" font="default" size="100%">Dephasing superchannels</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Krzysztof Domino</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Mátyás Koniorczyk</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Statistical quality assessment of Ising-based annealer outputs</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2022</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Quantum Information Processing</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">21</style></VOLUME><SECTION><style face="normal" font="default" size="100%">228</style></SECTION><DATE><style face="normal" font="default" size="100%">08/2022</style></DATE><URL><style face="normal" font="default" size="100%">https://doi.org/10.1007/s11128-022-03623-5</style></URL><title><style face="normal" font="default" size="100%">Statistical quality assessment of Ising-based annealer outputs</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Koorosh Sadri</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Fereshte Shahbeigi</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Karol Życzkowski</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Accessible maps in a group of classical or quantum channels</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2022</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%"/></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">29</style></VOLUME><SECTION><style face="normal" font="default" size="100%">2250002</style></SECTION><DATE><style face="normal" font="default" size="100%">08/2022</style></DATE><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;We study the problem of accessibility in a set of classical and quantum channels admitting a group structure. Group properties of the set of channels, and the structure of the closure of the analyzed group &lt;em&gt;G&lt;/em&gt; plays a pivotal role in this regard. The set of all convex combinations of the group elements contains a subset of channels that are accessible by a dynamical semigroup. We demonstrate that accessible channels are determined by probability vectors of weights of a convex combination of the group elements, which depend neither on the dimension of the space on which the channels act, nor on the specific representation of the group. Investigating geometric properties of the set &lt;em&gt;A&lt;/em&gt; of accessible maps we show that this set is non-convex, but it enjoys the star-shape property with respect to the uniform mixture of all elements of the group. We demonstrate that the set &lt;em&gt;A&lt;/em&gt; covers a positive volume in the polytope of all convex combinations of the elements of the group.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://doi.org/10.1142/S1230161222500020</style></URL><title><style face="normal" font="default" size="100%">Accessible maps in a group of classical or quantum channels</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Tomasz Śmierzchalski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Tomasz Trzciński</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Bartłomiej Gardas</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Post-Error Correction for Quantum Annealing Processor using Reinforcement Learning</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2022</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">International Conference on Computational Science (ICCS 2022): Lecture Notes in Computer Science </style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><SECTION><style face="normal" font="default" size="100%">261–268</style></SECTION><DATE><style face="normal" font="default" size="100%">07/2022</style></DATE><URL><style face="normal" font="default" size="100%">https://link.springer.com/chapter/10.1007/978-3-031-08760-8_22</style></URL><title><style face="normal" font="default" size="100%">Post-Error Correction for Quantum Annealing Processor using Reinforcement Learning</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Paulina Lewandowska</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Ryszard Kukulski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Storage and retrieval of von Neumann measurements</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2022</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Physical Review A</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">106</style></VOLUME><ISSUE><style face="normal" font="default" size="100%">5</style></ISSUE><SECTION><style face="normal" font="default" size="100%">052423</style></SECTION><DATE><style face="normal" font="default" size="100%">10/2022</style></DATE><URL><style face="normal" font="default" size="100%">https://arxiv.org/abs/2204.03029</style></URL><title><style face="normal" font="default" size="100%">Storage and retrieval of von Neumann measurements</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Ryszard Kukulski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">On the probabilistic quantum error correction</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2023</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">IEEE Transactions on Information Theory</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">69</style></VOLUME><ISSUE><style face="normal" font="default" size="100%">7</style></ISSUE><SECTION><style face="normal" font="default" size="100%">4620-4640</style></SECTION><DATE><style face="normal" font="default" size="100%">07/2023</style></DATE><URL><style face="normal" font="default" size="100%">https://arxiv.org/abs/2206.05232</style></URL><title><style face="normal" font="default" size="100%">On the probabilistic quantum error correction</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Paulina Lewandowska</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Strategies for single-shot discrimination of process matrices</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2023</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Scientific Reports</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">13</style></VOLUME><SECTION><style face="normal" font="default" size="100%">3046</style></SECTION><DATE><style face="normal" font="default" size="100%">02/2023</style></DATE><URL><style face="normal" font="default" size="100%">https://doi.org/10.1038/s41598-023-30191-0</style></URL><title><style face="normal" font="default" size="100%">Strategies for single-shot discrimination of process matrices</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Aleksandra Krawiec</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Discrimination and certification of unknown quantum measurements</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2024</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Quantum</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">8</style></VOLUME><SECTION><style face="normal" font="default" size="100%">1269</style></SECTION><DATE><style face="normal" font="default" size="100%">02/2024</style></DATE><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;&lt;span style="font-family:sans-serif; font-size:14.944px"&gt;We study the discrimination of von Neumann measurement in the scenario&lt;/span&gt;&lt;span style="font-family:sans-serif; font-size:14.944px"&gt; when we are given a reference measurement and some other measurement. The aim of&lt;/span&gt;&lt;span style="font-family:sans-serif; font-size:14.944px"&gt; the discrimination is to determine whether the other measurement is the same as the&lt;/span&gt;&lt;span style="font-family:sans-serif; font-size:14.944px"&gt; first one. We consider the cases when the reference measurement is given without the&lt;/span&gt;&lt;span style="font-family:sans-serif; font-size:14.944px"&gt; classical description and when its classical description is known. Both cases are studied&lt;/span&gt;&lt;span style="font-family:sans-serif; font-size:14.944px"&gt; in the symmetric and asymmetric discrimination setups. Moreover, we provide optimal&lt;/span&gt;&lt;span style="font-family:sans-serif; font-size:14.944px"&gt; certification schemes enabling us to certify a known quantum measurement against the&lt;/span&gt;&lt;span style="font-family:sans-serif; font-size:14.944px"&gt; unknown one.&lt;/span&gt;&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://doi.org/10.22331/q-2024-02-29-1269</style></URL><title><style face="normal" font="default" size="100%">Discrimination and certification of unknown quantum measurements</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Filip Maciejewski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Michał Oszmaniec</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Exploring Quantum Average-Case Distances: Proofs, properties, and examples</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2023</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">IEEE Transactions on Information Theory</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><URL><style face="normal" font="default" size="100%">https://doi.org/10.1109/TIT.2023.3250100</style></URL><title><style face="normal" font="default" size="100%">Exploring Quantum Average-Case Distances: Proofs, properties, and examples</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Filip Maciejewski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Michał Oszmaniec</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Operational Quantum Average-Case Distances</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2023</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Quantum</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">7</style></VOLUME><SECTION><style face="normal" font="default" size="100%">1106</style></SECTION><URL><style face="normal" font="default" size="100%">https://doi.org/10.22331/q-2023-09-11-1106</style></URL><title><style face="normal" font="default" size="100%">Operational Quantum Average-Case Distances</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Hanna Wojewódka-Ściążko</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Kamil Korzekwa</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Resource engines</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2024</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Quantum</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">8</style></VOLUME><SECTION><style face="normal" font="default" size="100%">1222</style></SECTION><DATE><style face="normal" font="default" size="100%">07/24</style></DATE><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we aim to push the analogy between thermodynamics and quantum resource theories one step further. Previous inspirations were based on thermodynamic considerations concerning scenarios with a single heat bath, neglecting an important part of thermodynamics that studies heat engines operating between two baths at different temperatures. Here, we investigate the performance of resource engines, which replace the access to two heat baths at different temperatures with two arbitrary constraints on state transformations. The idea is to imitate the action of a two--stroke heat engine, where the system is sent to two agents (Alice and Bob) in turns, and they can transform it using their constrained sets of free operations. We raise and address several questions, including whether or not a resource engine can generate a full set of quantum operations or all possible state transformations, and how many strokes are needed for that. We also explain how the resource engine picture provides a natural way to fuse two or more resource theories, and we discuss in detail the fusion of two resource theories of thermodynamics with two different temperatures, and two resource theories of coherence with respect to two different bases.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://doi.org/10.22331/q-2024-01-10-1222</style></URL><title><style face="normal" font="default" size="100%">Resource engines</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Tomasz Śmierzchalski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Jakub Pawłowski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Artur Przybysz</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Mátyás Koniorczyk</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Bartłomiej Gardas</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Sebastian Deffner</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Krzysztof Domino</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Hybrid quantum-classical computation for automatic guided vehicles scheduling</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2024</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Scientific Reports</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">14</style></VOLUME><SECTION><style face="normal" font="default" size="100%">21809</style></SECTION><DATE><style face="normal" font="default" size="100%">09/2014</style></DATE><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;Motivated by recent efforts to develop quantum computing for practical, industrial-scale challenges, we demonstrate the effectiveness of state-of-the-art hybrid (not necessarily quantum) solvers in addressing the business-centric optimization problem of scheduling Automatic Guided Vehicles (AGVs). Some solvers can already leverage noisy intermediate-scale quantum (NISQ) devices. In our study, we utilize D-Wave hybrid solvers that implement classical heuristics with potential assistance from a quantum processing unit. This hybrid methodology performs comparably to existing classical solvers. However, due to the proprietary nature of the software, the precise contribution of quantum computation remains unclear. Our analysis focuses on a practical, business-oriented scenario: scheduling AGVs within a factory constrained by limited space, simulating a realistic production setting. Our approach maps a realistic AGVs problem onto one reminiscent of railway scheduling and demonstrates that the AGVs problem is better suited to quantum computing than its railway counterpart, the latter being denser in terms of the average number of constraints per variable. The main idea here is to highlight the potential usefulness of a hybrid approach for handling AGVs scheduling problems of practical sizes. We show that a scenario involving up to 21 AGVs, significant due to possible deadlocks, can be efficiently addressed by a hybrid solver in seconds.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://rdcu.be/dUkwi</style></URL><title><style face="normal" font="default" size="100%">Hybrid quantum-classical computation for automatic guided vehicles scheduling</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>31</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Bartłomiej Gardas</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Przemysław Głomb</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Przemysław Sadowski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Konrad Jałowiecki</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Orphee Faucoz</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Pierre-Marie Brunet</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Piotr Gawron</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Matthijs Van Waveren</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Mickaël Savinaud</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Guillaume Pasero</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Veronique Defonte</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Hyper-Spectral Image Classification Using Adiabatic Quantum Computation</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2023</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">IGARSS 2023 - 2023 IEEE International Geoscience and Remote Sensing Symposium</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><title><style face="normal" font="default" size="100%">Hyper-Spectral Image Classification Using Adiabatic Quantum Computation</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>31</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Matthijs Van Waveren</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Mickaël Savinaud</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Guillaume Pasero</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Veronique Defonte</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Pierre-Marie Brunet</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Orphee Faucoz</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Piotr Gawron</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Bartłomiej Gardas</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Comparison of Quantum Neural Network Algorithms For Earth Observation Data Classification</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2023</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">IGARSS 2023 - 2023 IEEE International Geoscience and Remote Sensing Symposium</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><title><style face="normal" font="default" size="100%">Comparison of Quantum Neural Network Algorithms For Earth Observation Data Classification</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Ryszard Kukulski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Mateusz Stępniak</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Kamil Hendzel</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Bartłomiej Gardas</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Local certification of unitary operations</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2024</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Scientific Reports</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><VOLUME><style face="normal" font="default" size="100%">14</style></VOLUME><SECTION><style face="normal" font="default" size="100%">26588</style></SECTION><title><style face="normal" font="default" size="100%">Local certification of unitary operations</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>31</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Piotr Gawron</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Przemysław Sadowski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Przemysław Głomb</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Bartłomiej Gardas</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Matthijs Van Waveren</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Clément Forray</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Guillaume Pasero</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Mickaël Savinaud</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Pierre-Marie Brunet</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Orphee Faucoz</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">What Could be Achieved with a Million Qubits Quantum Annealer in Remote Sensing?</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2024</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">IGARSS 2024-2024 IEEE International Geoscience and Remote Sensing Symposium</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><title><style face="normal" font="default" size="100%">What Could be Achieved with a Million Qubits Quantum Annealer in Remote Sensing?</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Marcin Markiewicz</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Single-shot comparison of random quantum channels and measurements</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2026</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Scientific Reports</style></SECONDARY_TITLE><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;In this work we provide an efficiency analysis of the problem of discrimination of two randomly chosen unknown quantum operations in the single-shot regime. We provide tight bounds for the success probability of such a protocol for arbitrary quantum channels and generalized measurements.&lt;/p&gt;&#13;
</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://www.nature.com/articles/s41598-026-70695-z</style></URL><title><style face="normal" font="default" size="100%">Single-shot comparison of random quantum channels and measurements</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>15</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Ryszard Kukulski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Quantum Probabilistic Error Correction Method</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2025</style></YEAR><PLACE_PUBLISHED><style face="normal" font="default" size="100%">United States of America</style></PLACE_PUBLISHED><LANGUAGE><style face="normal" font="default" size="100%">eng</style></LANGUAGE><SECTION><style face="normal" font="default" size="100%">US 12,299,539 B2</style></SECTION><DATE><style face="normal" font="default" size="100%">05/2025</style></DATE><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;A quantum computer implemented probabilistic error correction method for use with quantum circuits with a noise channel N(X) that has a Choi rank not greater than two, such as N(X)=N0XN0†+N1XN1†. The method comprising steps of: encoding a first qubit into an encoded state ?ψ , putting a second qubit into an arbitrary fixed state ?d1 , implementing two qubit unitary operation UE on the first qubit and the second qubit to obtain an encoded state UE(?ψ ^?d1 ), and after the encoded state is affected by the noise N(X), implementing two qubit unitary operation UD, followed by measuring the second qubit in the {?d2 , ?d2⊥ } basis measurement to obtain a classical label i∈{0,1}, next preparing a third qubit in the arbitrary fixed state ?d3 , and implementing two qubit unitary operation VD on the first qubit and the third qubit, followed by measuring the third qubit in the {?d4 , ?d4⊥ } basis measurement to obtain a classical label j∈{0,1}, and when (i,j)=(0,0) accepting as an output δexp a decoded state of the first qubit, and when (i,j)≠(0,0) rejecting the output δexp of a decoded state of the first qubit.&lt;/p&gt;&#13;
</style></ABSTRACT><title><style face="normal" font="default" size="100%">Quantum Probabilistic Error Correction Method</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Adam Bílek</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Ryszard Kukulski</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Paulina Lewandowska</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Noise Resilience of Quantum Key Distribution Protocols Secured Against Independent Attacks With One-Way Communication</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2026</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">arXiv:2607.11857</style></SECONDARY_TITLE><PAGES><style face="normal" font="default" size="100%">19</style></PAGES><DATE><style face="normal" font="default" size="100%">07/10/2026</style></DATE><ABSTRACT><style face="normal" font="default" size="100%">We investigate the resilience to noise of single-qubit quantum key distribution (QKD) protocols in the scenario of security against independent eavesdropping attacks and key distillation based on one-way classical communication. To this end, we introduce a noise-based metric that quantifies the efficiency of QKD protocols. Within this framework, we analyze the maximal noise levels that allow Alice and Bob to asymptotically establish a secure secret key. Using this assumption, we compare the noise tolerance of general single-qubit QKD protocols, in particular the BB84, B92, E91, and six-state protocols. Our main result determines the noise level threshold for QKD allowing one to distill an asymptotically secure secret key. Additionally, we demonstrate that the six-state protocol achieves the greatest resistance to noise while simultaneously yielding a higher post-selection efficiency than the other analyzed single-qubit protocols, confirming its robustness within the considered security model. Finally, we perform an analysis of the proposed noise-based metric and the conventional quantum bit error rate (QBER) metric.</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://arxiv.org/abs/2607.11857</style></URL><title><style face="normal" font="default" size="100%">Noise Resilience of Quantum Key Distribution Protocols Secured Against Independent Attacks With One-Way Communication</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Ludmiła Marcinkowska</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Marcin Markiewicz</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Asymptotic distinguishability of Haar-averaged measurement models</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2026</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">arXiv:2605.31168</style></SECONDARY_TITLE><PAGES><style face="normal" font="default" size="100%">49</style></PAGES><DATE><style face="normal" font="default" size="100%">05/29/2026</style></DATE><ABSTRACT><style face="normal" font="default" size="100%">We study discrimination problems generated by the same basic Haar-random measurement mechanism at two observational levels. First, we derive an explicit expression for the type-II error in the task of discriminating a Haar-random measure-and-prepare channel from the identity channel I, using a coherence-sensitive entangled tester. Second, after passing to the induced classical measurement records, we compare two random measurement models: one induced by a single collective unitary of the form U^⊗(n₁+n₂) with U ∈ U(d), and another induced by independent local unitaries U₁^⊗n₁ ⊗ U₂^⊗n₂. For the associated Haar-averaged aggregate histogram laws, in which the block of origin of each count is not retained, we obtain closed-form formulas and quantify their discrepancy through the total variation distance. We derive asymptotic expressions in the fixed-N, large-d regime, the fixed-d, large-N regime, the sparse joint-scaling regime N = o(√d), and the critical scaling regime N/√d → c. We also identify the block-resolved pair-of-histograms law, showing that the aggregate total variation distance is a coarse-grained lower bound on the distinguishability available when block labels are retained.</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://arxiv.org/abs/2605.31168</style></URL><title><style face="normal" font="default" size="100%">Asymptotic distinguishability of Haar-averaged measurement models</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">IntegrateUnitary.jl: A Julia package for symbolic integration over Haar measures</style></TITLE></TITLES><KEYWORDS><KEYWORD><style face="normal" font="default" size="100%">Symbolic integration; Haar measure; Weingarten calculus; Julia programming language; quantum information</style></KEYWORD></KEYWORDS><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2026</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">arXiv:2605.23830</style></SECONDARY_TITLE><DATE><style face="normal" font="default" size="100%">06/2026</style></DATE><TYPE_OF_WORK><style face="normal" font="default" size="100%">Manuscript submitted to ACM</style></TYPE_OF_WORK><KEYWORD><style face="normal" font="default" size="100%"/></KEYWORD><ABSTRACT><style face="normal" font="default" size="100%">Symbolic integration over the Haar measure of compact groups is a computational cornerstone in quantum information science and random matrix theory. We present IntegrateUnitary.jl, a comprehensive Julia package for computing exact expectations of polynomial functions over a wide range of compact groups (U(d), O(d), Sp(d), and SU(d) for balanced polynomials), circular and Gaussian ensembles, Ginibre ensembles, permutation groups, random pure states, and unitary t-designs. The package provides a fully open-source implementation of the Weingarten calculus and Wick contractions with broad symbolic-d support for entry-wise and trace-polynomial integrals, while selected workflows currently require concrete integer dimensions (including higher pure trace moments |tr(U)|^2k for k &gt; 1 and HCIZ with SymbolicMatrix inputs, and direct matrix-valued integration of SymbolicMatrix/SymbolicMatrixProduct expressions), automatic asymptotic expansions, a high-level symbolic trace interface that reconstructs Weingarten graphs from index-free expressions, and a bridge to ITensors.jl for tensor network averaging. We discuss the underlying algorithms, including the Murnaghan-Nakayama rule and symplectic-orthogonal duality, and demonstrate that the package efficiently handles high-degree moments and quantum information metrics.</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://arxiv.org/abs/2605.23830</style></URL><title><style face="normal" font="default" size="100%">IntegrateUnitary.jl: A Julia package for symbolic integration over Haar measures</style></title></RECORD><RECORD><source-app name="Bibcite" version="8.x">Drupal-Bibcite</source-app><REFERENCE_TYPE>0</REFERENCE_TYPE><CONTRIBUTORS><AUTHORS><AUTHOR><style face="normal" font="default" size="100%">Marcin Markiewicz</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Łukasz Pawela</style></AUTHOR><AUTHOR><style face="normal" font="default" size="100%">Zbigniew Puchała</style></AUTHOR></AUTHORS></CONTRIBUTORS><TITLES><TITLE><style face="normal" font="default" size="100%">Choi-level twirling of quantum channels: finite constructions and non-compact transformations</style></TITLE></TITLES><KEYWORDS/><DATES/><AUTHORS><style face="normal" font="default" size="100%"/></AUTHORS><YEAR><style face="normal" font="default" size="100%">2026</style></YEAR><SECONDARY_TITLE><style face="normal" font="default" size="100%">Journal of Physics A: Mathematical and Theoretical</style></SECONDARY_TITLE><PAGES><style face="normal" font="default" size="100%">15</style></PAGES><DATE><style face="normal" font="default" size="100%">25/02/2026</style></DATE><TYPE_OF_WORK><style face="normal" font="default" size="100%">artykuł w czasopiśmie</style></TYPE_OF_WORK><ABSTRACT><style face="normal" font="default" size="100%">&lt;p&gt;Twirling, i.e. averaging over symmetry actions, is a standard tool for reducing quantum states and channels to a symmetry-invariant form. We study channel twirling from the perspective of the channel–state duality and provide a constructive Choi-level description of the averaging map induced by arbitrary input/output representations. Our main technical result concerns the collective setting: for π &lt;sup&gt;in&lt;/sup&gt;(U) = U &lt;sup&gt;⊗t&lt;/sup&gt;&lt;sub&gt;&lt;sup&gt;in&lt;/sup&gt;&lt;/sub&gt; and π &lt;sup&gt;out&lt;/sup&gt;(U) = U &lt;sup&gt;⊗t&lt;/sup&gt;&lt;sub&gt;&lt;sup&gt;out&lt;/sup&gt;&lt;/sub&gt; , we introduce a partial-transpose reduction that removes the contragredient action and converts the mixed (walled Brauer) channel twirl into an ordinary Schur–Weyl twirl of the partially transposed Choi operator under U &lt;sup&gt;⊗(t&lt;/sup&gt;&lt;sub&gt;&lt;sup&gt;in&lt;/sup&gt;&lt;/sub&gt;&lt;sup&gt;+t&lt;/sup&gt;&lt;sub&gt;&lt;sup&gt;out&lt;/sup&gt;&lt;/sub&gt;&lt;sup&gt;)&lt;/sup&gt; , enabling explicit permutation-based formulas without constructing walled Brauer idempotents or mixed Schur transforms. Beyond compact symmetries, we extend channel twirling to reductive, generally non-unitary groups via Cartan decomposition and obtain an invariant-sector decomposition of the averaged Choi operator with weights determined solely by the Abelian Cartan component. Finally, we provide two finite realizations of channel averaging: a “dual” implementation as a convex mixture of unitary-1-design channels acting on invariant sectors, and a design-like reconstruction showing that weighted group t-designs induce channel t-designs for t = t&lt;sub&gt;in&lt;/sub&gt; + t&lt;sub&gt;out&lt;/sub&gt;.&lt;/p&gt;</style></ABSTRACT><URL><style face="normal" font="default" size="100%">https://arxiv.org/abs/2512.23586</style></URL><title><style face="normal" font="default" size="100%">Choi-level twirling of quantum channels: finite constructions and non-compact transformations</style></title></RECORD></records></xml>
