01106nas a2200157   4500000000100000000000100001008004100002100002300043700001900066700002200085700002200107245004600129856004000175490000700215520072600222       2016                            d1 aRadosław Adamczak1 aRafał Latała1 aZbigniew Puchała1 aKarol Życzkowski00aAsymptotic entropic uncertainty relations  uhttp://dx.doi.org/10.1063/1.49444250 v573 a<p>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.</p>
01167nas a2200205   4500000000100000000000100001000000100002008004100003100001800044700001700062700001800079700002200097700002200119700002200141245005200163300001100215490000700226520071400233022001400947       2011                            d1 aCharles Dunkl1 aPiotr Gawron1 aJ.A. Holbrook1 aJaroslaw Miszczak1 aZbigniew Puchała1 aKarol Życzkowski00aNumerical shadow and geometry of quantum states  a3353010 v443 aThe 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.  a1751-811301687nas a2200181   4500000000100000000000100001008004100002100001800043700001700061700001800078700002200096700002200118245006900140300001600209490000800225520125800233022001401491       2011                            d1 aCharles Dunkl1 aPiotr Gawron1 aJ.A. Holbrook1 aZbigniew Puchała1 aKarol Życzkowski00aNumerical shadows: measures and densities on the numerical range  a2042–20800 v4343 aFor 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.  a0024-379500470nas a2200181   4500000000100000000000100001008004100002100001800043700001700061700001900078700002200097700002200119245005200141856004600193300001200239490000800251520002900259       2015                            d1 aCharles Dunkl1 aPiotr Gawron1 aŁukasz Pawela1 aZbigniew Puchała1 aKarol Życzkowski00aReal numerical shadow and generalized B-splines  uhttps://doi.org/10.1016/j.laa.2015.03.029  a12–510 v4793 a<p>arXiv:1409.4941</p>
01465nas a2200169   4500000000100000000000100001000000100002008004100003100001700044700002200061700002200083245007400105856003800179300001600217490000700233520105500240       2015                            d1 aM. Enríquez1 aZbigniew Puchała1 aKarol Życzkowski00aMinimal Renyi-Ingarden-Urbanik entropy of multipartite quantum states  uhttps://doi.org/10.3390/e17075063  a5063–50840 v173 a<p>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.</p>
00594nas a2200133   4500000000100000000000100001008004100002100002300043700002200066245006700088300001100155490000700166520028700173       2012                            d1 aBartłomiej Gardas1 aZbigniew Puchała00aNotes on the Riccati operator equation in open quantum systems  a0121060 v533 a<p>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.</p>
00672nas a2200145   4500000000100000000000100001000000100002008004100003100002300044700002200067245005600089300001100145490000700156520036300163       2011                            d1 aBartłomiej Gardas1 aZbigniew Puchała00aStationary states of two-level open quantum systems  a2153060 v443 a<p>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.</p>
00938nas a2200205   4500000000100000000000100001008004100002260003400043100001700077700002300094700002200117700002200139700002400161700002500185700002200210245005500232300001200287520041100299020002200710       2011                            d  bSpringeraBerlin / Heidelberg1 aPiotr Gawron1 aPrzemysław Głomb1 aJaroslaw Miszczak1 aZbigniew Puchała1 aTadeusz Czachórski1 aStanisław Kozielski1 aUrszula Stańczyk00aEigengestures for natural human computer interface  a49–563 aWe 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.  a978-3-642-23168-100323nas a2200157   4500000000100000000000100001000000100002008004100003100001700044700001900061700002200080245003000102300001200132490000700144022001400151       2013                            d1 aPiotr Gawron1 aDariusz Kurzyk1 aZbigniew Puchała00aA model for quantum queue  a13500230 v11  a0219-749900444nas a2200181   4500000000100000000000100001000000100002008004100003100001700044700002200061700002200083700001800105700002200123245008600145300001100231490000700242022001300249       2010                            d1 aPiotr Gawron1 aZbigniew Puchała1 aJaroslaw Miszczak1 aŁ. Skowronek1 aKarol Życzkowski00aRestricted numerical range: A versatile tool in the theory of quantum information  a1022040 v51  a0022248801225nas a2200169   4500000000100000000000100001000000100002008004100003100002300044700002200067700002100089245008600110300001400196490000700210520081700217022002101034       2007                            d1 aPrzemysław Głomb1 aZbigniew Puchała1 aArkadiusz Sochan00aContext selection for efficient bit modeling of contourlet transform coefficients  a135–1460 v193 aContourlet 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  aISSN 1896–533401585nas a2200157   4500000000100000000000100001008004100002100002200043700002200065700002200087245007200109856004700181300001100228490000700239520118100246       2014                            d1 aA. Lakshminarayan1 aZbigniew Puchała1 aKarol Życzkowski00aDiagonal unitary entangling gates and contradiagonal quantum states  uhttps://doi.org/10.1103/PhysRevA.90.032303  a0323030 v903 a<p>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</p>
01214nas a2200181   4500000000100000000000100001000000100002008004100003100001500044700002200059700002200081700002200103245005500125300001100180490000700191520082000198022001401018       2008                            d1 aD. Markham1 aJaroslaw Miszczak1 aZbigniew Puchała1 aKarol Życzkowski00aQuantum state discrimination: A geometric approach  a0421110 v773 aWe 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.  a1094-162200723nas a2200157   4500000000100000000000100001000000100002008004100003100002200044700001700066700002200083245004700105300001600152490000700168520039000175       2012                            d1 aJaroslaw Miszczak1 aPiotr Gawron1 aZbigniew Puchała00aQubit flip game on a Heisenberg spin chain  a1571–15830 v113 aWe 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.01219nas a2200205   4500000000100000000000100001000000100002008004100003260000600044100002200050700002200072700002100094700001500115700002200130245005900152300001600211490000600227520076600233022001400999       2009                            d  c11 aJaroslaw Miszczak1 aZbigniew Puchała1 aPaweł Horodecki1 aA. Uhlmann1 aKarol Życzkowski00aSub- and super-fidelity as bounds for quantum fidelity  a0103–01300 v93 aWe 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.  a1533-714600340nas a2200145   4500000000100000000000100001008004100002100001900043700001700062700002200079700002000101245005600121300001100177490000600188       2013                            d1 aŁukasz Pawela1 aPiotr Gawron1 aZbigniew Puchała1 aJan Sładkowski00aEnhancing pseudo-telepathy in the Magic Square game  ae646940 v800768nas a2200133   4500000000100000000000100001008004100002100001900043700002200062245008000084856004600164490000700210520041700217       2016                            d1 aŁukasz Pawela1 aZbigniew Puchała00aQuantifying channels output similarity with applications to quantum control  uhttps://doi.org/10.1007/s11128-015-1238-z0 v153 a<p>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.</p>
00379nas a2200145   4500000000100000000000100001000000100002008004100003100001900044700002200063245008100085856004600166300001400212490000700226       2015                            d1 aŁukasz Pawela1 aZbigniew Puchała00aQuantum control robust with respect to coupling with an external environment  uhttps://doi.org/10.1007/s11128-014-0879-7  a437–4460 v1401256nas a2200145   4500000000100000000000100001008004100002100001900043700002200062245004600084856004600130300001400176490000700190520091300197       2014                            d1 aŁukasz Pawela1 aZbigniew Puchała00aQuantum control with spectral constraints  uhttps://doi.org/10.1007/s11128-013-0644-3  a227–2370 v133 a<p>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.</p>
00745nas a2200133   4500000000100000000000100001000000100002008004100003100002200044245004500066300001400111490000700125520047900132       2013                            d1 aZbigniew Puchała00aLocal controllability of quantum systems  a459–4660 v123 aWe 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.00420nas a2200133   4500000000100000000000100001000000100002008004100003100002200044245005900066300001400125490000700139520014000146       2005                            d1 aZbigniew Puchała00aProof of Grabiner's theorem on non-colliding particles  a129–1320 v253 aA detail proof of Grabiner's theorem [1] on the exact asymptotics of the time to collision for n independent Brownian motions is given.01088nas a2200205   4500000000100000000000100001000000100002008004100003100002200044700001700066700002200083700001800105700001800123700002200141245006900163300001400232490000800246520061400254022001400868       2011                            d1 aZbigniew Puchała1 aPiotr Gawron1 aJaroslaw Miszczak1 aŁ. Skowronek1 aMan-Duen Choi1 aKarol Życzkowski00aProduct numerical range in a space with tensor product structure  a327–3420 v4343 aWe 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.  a0024-379501268nas a2200169   4500000000100000000000100001008004100002100002200043700001500065700001400080700001300094245008900107856004700196300001100243490000700254520083700261       2015                            d1 aZbigniew Puchała1 aA. Jencova1 aM. Sedlak1 aM. Ziman00aExploring boundaries of quantum convex structures: Special role of unitary processes  uhttps://doi.org/10.1103/PhysRevA.92.012304  a0123040 v923 a<p>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.</p>
00682nas a2200133   4500000000100000000000100001008004100002100002200043700002200065245005500087300001100142490000700153520038800160       2011                            d1 aZbigniew Puchała1 aJaroslaw Miszczak00aProbability measure generated by the superfidelity  a4053010 v443 aWe 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.00790nas a2200145   4500000000100000000000100001008004100002260001200043100002200055700002200077245008000099856004500179490000700224520041300231       2017                            d  c02/20171 aZbigniew Puchała1 aJaroslaw Miszczak00aSymbolic integration with respect to the Haar measure on the unitary groups  uhttps://doi.org/10.1515/bpasts-2017-00030 v653 a<p>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.</p>
00645nas a2200133   4500000000100000000000100001008004100002100002200043700002200065245005100087300001100138490000700149520035500156       2009                            d1 aZbigniew Puchała1 aJaroslaw Miszczak00aBound on trace distance based on superfidelity  a0243020 v793 aWe 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.01853nas a2200181   4500000000100000000000100001008004100002100002200043700002200065700001700087700001800104700001800122700002200140245006900162300001100231490000700242520142200249       2012                            d1 aZbigniew Puchała1 aJaroslaw Miszczak1 aPiotr Gawron1 aCharles Dunkl1 aJ.A. Holbrook1 aKarol Życzkowski00aRestricted numerical shadow and geometry of quantum entanglement  a4153090 v453 aThe 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> 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.01187nas a2200181   4500000000100000000000100001000000100002008004100003100002200044700002200066700001700088700002300105245007600128300001100204490000700215520076900222022001400991       2011                            d1 aZbigniew Puchała1 aJaroslaw Miszczak1 aPiotr Gawron1 aBartłomiej Gardas00aExperimentally feasible measures of distance between quantum operations  a1–120 v103 a<p>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.</p>
  a1570-075501220nas a2200145   4500000000100000000000100001008004100002100002200043700001900065700002200084245004900106856004700155490000700202520086500209       2016                            d1 aZbigniew Puchała1 aŁukasz Pawela1 aKarol Życzkowski00aDistinguishability of generic quantum states  uhttps://doi.org/10.1103/PhysRevA.93.0621120 v933 a<p>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&nbsp;=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.</p>
00364nas a2200133   4500000000100000000000100001008004100002260000700043100002200050700001400072245012200086300001400208490000800222       2008                            d  c111 aZbigniew Puchała1 aT. Rolski00aThe exact asymptotic of the collision time tail distribution for independent Brownian particles with different drifts  a595–6170 v3-400758nas a2200157   4500000000100000000000100001000000100002008004100003260000700044100002200051700001400073245005000087300001600137490000700153520044000160       2005                            d  c111 aZbigniew Puchała1 aT. Rolski00aThe exact asymptotic of the time to collision  a1359–13800 v103 aAbstract 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.00948nas a2200181   4500000000100000000000100001008004100002100002200043700001700065700001500082700001600097700002200113245007500135856004700210300001100257490000700268520049100275       2015                            d1 aZbigniew Puchała1 aŁ. Rudnicki1 aK. Chabuda1 aM. Paraniak1 aKarol Życzkowski00aCertainty relations, mutual entanglement and non-displacable manifolds  uhttps://doi.org/10.1103/PhysRevA.92.032109  a0321090 v923 a<p>{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</p>
01158nas a2200145   4500000000100000000000100001008004100002100002200043700001700065700002200082245004800104300001100152490000700163520084200170       2013                            d1 aZbigniew Puchała1 aŁ. Rudnicki1 aKarol Życzkowski00aMajorization entropic uncertainty relations  a2720020 v463 aEntropic 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.01182nas a2200169   4500000000100000000000100001000000100002008004100003100001800044700002200062700001700084700002200101245005600123300001100179490000700190520081500197       2013                            d1 aWojciech Roga1 aZbigniew Puchała1 aŁ. Rudnicki1 aKarol Życzkowski00aEntropic trade-off relations for quantum operations  a0323080 v873 aSpectral 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.01054nas a2200181   4500000000100000000000100001000000100002008004100003100001700044700002200061700002100083700002200104245006000126856005100186300001100237490000700248520061700255       2014                            d1 aŁ. Rudnicki1 aZbigniew Puchała1 aPaweł Horodecki1 aKarol Życzkowski00aConstructive entanglement test from triangle inequality  uhttps://doi.org/10.1088/1751-8113/47/42/424035  a4240350 v473 a<p>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'.</p>
01086nas a2200169   4500000000100000000000100001000000100002008004100003100001700044700002200061700002100083700002200104245004400126300001100170490000700181520072800188       2012                            d1 aŁ. Rudnicki1 aZbigniew Puchała1 aPaweł Horodecki1 aKarol Życzkowski00aCollectibility for Mixed Quantum States  a0623290 v863 aBounds 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.01301nas a2200169   4500000000100000000000100001000000100002008004100003100001700044700002200061700002200083245005500105856004700160300001100207490000700218520090600225       2014                            d1 aŁ. Rudnicki1 aZbigniew Puchała1 aKarol Życzkowski00aStrong Majorization Entropic Uncertainty Relations  uhttps://doi.org/10.1103/PhysRevA.89.052115  a0521150 v893 a<p>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</p>
00441nas a2200181   4500000000100000000000100001000000100002008004100003100002300044700001700067700002200084700001900106700002200125245007900147300001200226490000700238022001400245       2013                            d1 aRyszard Winiarczyk1 aPiotr Gawron1 aJaroslaw Miszczak1 aŁukasz Pawela1 aZbigniew Puchała00aAnalysis of patent activity in the field of quantum information processing  a13500070 v11  a0219-749900846nas a2200157   4500000000100000000000100001000000100002008004100003100001600044700002200060700002200082245009200104300001400196490000700210520047100217       2013                            d1 aP. Zawadzki1 aZbigniew Puchała1 aJaroslaw Miszczak00aIncreasing the security of the ping-pong protocol by using many mutually unbiased bases  a569–5760 v123 aIn 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.00390nas a2200157   4500000000100000000000100001008004100002100001700043700001900060700002200079700002000101700002200121245006800143300001400211490000700225       2015                            d1 aPiotr Gawron1 aŁukasz Pawela1 aZbigniew Puchała1 aJacek Szklarski1 aKarol Życzkowski00aWybory samorządowe 2014 w poszukiwaniu anomalii statystycznych  a534–5450 v3001373nas a2200169   4500000000100000000000100001008004100002100001600043700002200059700001900081700002200100245004800122856003800170300001100208490000700219520097700226       2018                            d1 aIon Nechita1 aZbigniew Puchała1 aŁukasz Pawela1 aKarol Życzkowski00aAlmost all quantum channels are equidistant  uhttps://doi.org/10.1063/1.5019322  a0522010 v593 a<p>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 <span style="font-size:129%">1/2<em>+2/π</em></span>. Furthermore, we show that for a random state <span style="font-size:129%"><em>ρ</em></span> 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 <span style="font-size:129%"><em>ρ</em></span> may be interpreted as a Jamio{\l}kowski state of a unital map.</p>
01165nas a2200169   4500000000100000000000100001008004100002100002200043700002200065700001900087700002300106700002200129245005700151856004700208490000700255520073300262       2017                            d1 aMarcin Markiewicz1 aZbigniew Puchała1 aAnna de Rosier1 aWiesław Laskowski1 aKarol Życzkowski00aQuantum noise generated by local random Hamiltonians  uhttps://doi.org/10.1103/PhysRevA.95.0323330 v953 a<p>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.</p>
00817nas a2200157   4500000000100000000000100001008004100002100002100043700002200064700002200086245006000108856004500168300000700213490000600220520043300226       2018                            d1 aŁukasz Rudnicki1 aZbigniew Puchała1 aKarol Życzkowski00aGauge invariant information concerning quantum channels  uhttps://doi.org/10.22331/q-2018-04-11-60  a600 v23 a<p>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.</p>
01050nas a2200157   4500000000100000000000100001008004100002100001900043700001900062700002200081245006900103856004600172300000800218490000700226520065900233       2018                            d1 aDariusz Kurzyk1 aŁukasz Pawela1 aZbigniew Puchała00aConditional entropic uncertainty relations for Tsallis entropies  uhttps://doi.org/10.1007/s11128-018-1955-1  a1930 v173 a<p>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.</p>
00428nas a2200157   4500000000100000000000100001008004100002100001400043700002300057700002100080700002200101245008700123856004600210300000700256490000700263       2018                            d1 aAdam Glos1 aAleksandra Krawiec1 aRyszard Kukulski1 aZbigniew Puchała00aVertices cannot be hidden from quantum spatial search for almost all random graphs  uhttps://doi.org/10.1007/s11128-018-1844-7  a810 v1701221nas a2200157   4500000000100000000000100001008004100002100002200043700002100065700002300086700002200109245006400131856004500195490000700240520081600247       2018                            d1 aZbigniew Puchała1 aŁukasz Rudnicki1 aAleksandra Krawiec1 aKarol Życzkowski00aMajorization uncertainty relations for mixed quantum states  uhttps://doi.org/10.1088/1751-8121/aab66c0 v513 a<p>Majorization uncertainty relations are generalized for an arbitrary mixed quantum state <span style="font-size:129%"><em>ρ</em></span> of a finite size <span style="font-size:129%"><em>N</em></span>. 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 <span style="font-size:129%"><em>ρ</em></span> and the entries of a unitary matrix <span style="font-size:129%"><em>U</em></span> 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.</p>
01890nas a2200181   4500000000100000000000100001008004100002260001200043100001900055700002700074700002200101700002200123245003300145856004500178300001100223490000700234520146700241       2018                            d  c04/20181 aKamil Korzekwa1 aStanisław Czachórski1 aZbigniew Puchała1 aKarol Życzkowski00aCoherifying quantum channels  uhttps://doi.org/10.1088/1367-2630/aaaff3  a0430280 v203 a<p>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 $d$.</p>
01254nas a2200193   4500000000100000000000100001008004100002100002200043700002400065700002200089700001900111700001700130700002200147245009300169856004700262300001100309490000700320520073300327       2018                            d1 aMarcin Markiewicz1 aAdrian Kolodziejski1 aZbigniew Puchała1 aAdam Rutkowski1 aTomasz Tylec1 aWieslaw Laskowski00aUnified approach to geometric and positive-map-based non-linear entanglement identifiers  uhttps://doi.org/10.1103/PhysRevA.97.042339  a0423390 v973 a<p>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.</p>
00913nas a2200157   4500000000100000000000100001008004100002100001900043700001900062700002200081245007400103856004600177300000800223490000700231520051700238       2018                            d1 aDariusz Kurzyk1 aŁukasz Pawela1 aZbigniew Puchała00aUnconditional Security of a K-State Quantum Key Distribution Protocol  uhttps://doi.org/10.1007/s11128-018-1998-3  a2280 v173 a<p>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.</p>
01717nas a2200157   4500000000100000000000100001008004100002100002200043700001900065700002300084700002100107245007800128856003700206490000700243520130900250       2018                            d1 aZbigniew Puchała1 aŁukasz Pawela1 aAleksandra Krawiec1 aRyszard Kukulski00aStrategies for optimal single-shot discrimination of quantum measurements  uhttps://arxiv.org/abs/1804.058560 v983 a<p>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.</p>
01551nas a2200157   4500000000100000000000100001008004100002100002200043700002200065700002200087245009300109856003900202300001100241490000800252520113300260       2019                            d1 aMichał Oszmaniec1 aFilip Maciejewski1 aZbigniew Puchała00aSimulating all quantum measurements using only projective measurements and postselection  uhttps://arxiv.org/abs/1807.08449v1  a0123510 v1003 a<p>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.</p>
01498nas a2200169   4500000000100000000000100001008004100002100002200043700001900065700002300084700002100107700002200128245007700150856006100227490000600288520103400294       2021                            d1 aZbigniew Puchała1 aŁukasz Pawela1 aAleksandra Krawiec1 aRyszard Kukulski1 aMichał Oszmaniec00aMultiple-shot and unambiguous discrimination of von Neumann measurements  uhttps://quantum-journal.org/papers/q-2021-04-06-425/pdf/0 v53 a<p>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.</p>
01353nas a2200169   4500000000100000000000100001008004100002100001900043700002700062700002200089700002200111245006900133856003700202300001100239490000700250520092600257       2019                            d1 aKamil Korzekwa1 aStanisław Czachórski1 aZbigniew Puchała1 aKarol Życzkowski00aDistinguishing classically indistinguishable states and channels  uhttps://arxiv.org/abs/1812.09083  a4753030 v523 a<p>We investigate an original family of quantum distinguishability problems, where the goal is to perfectly distinguish between <span style="font-size:129%"><em>M</em></span> quantum states that become identical under a completely decohering map. Similarly, we study distinguishability of <span style="font-size:129%"><em>M</em></span> 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 <span style="font-size:129%"><em>M</em></span> perfectly distinguishable states (channels) that are classically indistinguishable.</p>
01400nas a2200157   4500000000100000000000100001008004100002100002200043700002100065700002200086245005600108856003700164300001400201490000800215520101900223       2019                            d1 aZbigniew Puchała1 aŁukasz Rudnicki1 aKarol Życzkowski00aPauli semigroups and unistochastic quantum channels  uhttps://arxiv.org/abs/1903.12448  a2376-23810 v3833 a<p>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, <span style="font-size:122%"><span style="font-family:stixgeneral">Φ</span><span style="font-family:stixgeneral">=</span><em>e</em><em>^{Lt}</em></span>,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.</p>
01737nas a2200169   4500000000100000000000100001008004100002260001300043100001900056700002200075700002100097700002200118245005800140856004800198490000700246520131400253       2022                            d  c03/2022 1 aKamil Korzekwa1 aZbigniew Puchała1 aMarco Tomamichel1 aKarol Życzkowski00aEncoding classical information into quantum resources  uhttps://dx.doi.org/10.1109/TIT.2022.31574400 v683 a<p>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.</p>
00286nas a2200121   4500000000100000000000100001008004100002100002300043700001900066700002200085245005000107490000700157       2020                            d1 aAleksandra Krawiec1 aŁukasz Pawela1 aZbigniew Puchała00aDiscrimination of POVMs with rank-one effects0 v1900419nas a2200157   4500000000100000000000100001008004100002260001200043100002300055700002500078700002200103700002300125245006800148856003800216490000700254       2021                            d  c07/20211 aFereshte Shahbeigi1 aDavid Amaro-Alcalá1 aZbigniew Puchała1 aKarol Życzkowski00aLog-Convex set of Lindblad semigroups acting on N -level system  uhttps://doi.org/10.1063/5.00097450 v6201326nas a2200157   4500000000100000000000100001008004100002100002400043700002300067700002100090700001900111700002200130245006100152490000700213520094800220       2021                            d1 aPaulina Lewandowska1 aAleksandra Krawiec1 aRyszard Kukulski1 aŁukasz Pawela1 aZbigniew Puchała00aOn the optimal certification of von Neumann measurements0 v113 a<p>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&nbsp;q-numerical range.</p>
00409nas a2200169   4500000000100000000000100001008004100002260001200043100002100055700001600076700001900092700002200111700002200133245003900155856003800194490000700232       2021                            d  c07/20211 aRyszard Kukulski1 aIon Nechita1 aŁukasz Pawela1 aZbigniew Puchała1 aKarol Życzkowski00aGenerating random quantum channels  uhttps://doi.org/10.1063/5.00388380 v6201608nas a2200157   4500000000100000000000100001008004100002100003200043700001900075700002200094700002200116245006800138856003800206490000700244520119900251       2022                            d1 aGrzegorz Rajchel-Mieldzioć1 aKamil Korzekwa1 aZbigniew Puchała1 aKarol Życzkowski00aAlgebraic and geometric structures inside the Birkhoff polytope  uhttps://doi.org/10.1063/5.00465810 v633 a<p>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.</p>
00403nas a2200145   4500000000100000000000100001008004100002260001200043100002300055700001900078700002200097245007200119856005900191490000700250       2021                            d  c11/20211 aAleksandra Krawiec1 aŁukasz Pawela1 aZbigniew Puchała00aExcluding false negative error in certification of quantum channels  uhttps://www.nature.com/articles/s41598-021-00444-x.pdf0 v1100275nas a2200121   4500000000100000000000100001008004100002100001900043700001900062700002200081245004300103490000700146       2021                            d1 aDariusz Kurzyk1 aŁukasz Pawela1 aZbigniew Puchała00aRelating entropies of quantum channels0 v2301790nas a2200181   4500000000100000000000100001008004100002260001200043100002200055700001900077700002000096700002100116700002200137245002800159856004800187490000800235520136500243       2021                            d  c11/20211 aZbigniew Puchała1 aKamil Korzekwa1 aRoberto Salazar1 aPaweł Horodecki1 aKarol Życzkowski00aDephasing superchannels  uhttps://doi.org/10.1103/PhysRevA.104.0526110 v1043 a<p>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 <em>E</em>, i.e., they leave invariant the transition probabilities induced by <em>E</em> 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(<em>E</em>) of a channel <em>E</em> 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 <em>E</em> by investigating the number of distinguishable channels that <em>E</em> 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 <em>E</em> and its fully dephased version, and also relate it to the robustness of coherence of <em>E</em>.</p>
00389nas a2200145   4500000000100000000000100001008004100002260001200043100002100055700002400076700002200100245006700122856004700189490000700236       2022                            d  c08/20221 aKrzysztof Domino1 aMátyás Koniorczyk1 aZbigniew Puchała00aStatistical quality assessment of Ising-based annealer outputs  uhttps://doi.org/10.1007/s11128-022-03623-50 v2101444nas a2200169   4500000000100000000000100001008004100002260001200043100001800055700002300073700002200096700002200118245006400140856004600204490000700250520101700257       2022                            d  c08/20221 aKoorosh Sadri1 aFereshte Shahbeigi1 aZbigniew Puchała1 aKarol Życzkowski00aAccessible maps in a group of classical or quantum channels  uhttps://doi.org/10.1142/S12301612225000200 v293 a<p>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 <em>G</em> 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 <em>A</em> 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 <em>A</em> covers a positive volume in the polytope of all convex combinations of the elements of the group.</p>
00479nas a2200157   4500000000100000000000100001008004100002260001200043100002600055700001900081700002200100700002200122700002300144245008700167856006700254       2022                            d  c07/20221 aTomasz Śmierzchalski1 aŁukasz Pawela1 aZbigniew Puchała1 aTomasz Trzciński1 aBartłomiej Gardas00aPost-Error Correction for Quantum Annealing Processor using Reinforcement Learning  uhttps://link.springer.com/chapter/10.1007/978-3-031-08760-8_2200398nas a2200157   4500000000100000000000100001008004100002260001200043100002400055700002100079700001900100700002200119245005400141856003700195490000800232       2022                            d  c10/20221 aPaulina Lewandowska1 aRyszard Kukulski1 aŁukasz Pawela1 aZbigniew Puchała00aStorage and retrieval of von Neumann measurements  uhttps://arxiv.org/abs/2204.030290 v10600383nas a2200157   4500000000100000000000100001008004100002260001200043100002100055700001900076700002200095245005000117856003700167490000700204022001400211       2023                            d  c07/20231 aRyszard Kukulski1 aŁukasz Pawela1 aZbigniew Puchała00aOn the probabilistic quantum error correction  uhttps://arxiv.org/abs/2206.052320 v69  a1557-965400386nas a2200145   4500000000100000000000100001008004100002260001200043100002400055700001900079700002200098245006600120856004700186490000700233       2023                            d  c02/20231 aPaulina Lewandowska1 aŁukasz Pawela1 aZbigniew Puchała00aStrategies for single-shot discrimination of process matrices  uhttps://doi.org/10.1038/s41598-023-30191-00 v1301543nas a2200169   4500000000100000000000100001008004100002260001200043100002300055700001900078700002200097245006900119856004700188490000600235520111800241022001401359       2024                            d  c02/20241 aAleksandra Krawiec1 aŁukasz Pawela1 aZbigniew Puchała00aDiscrimination and certification of unknown quantum measurements  uhttps://doi.org/10.22331/q-2024-02-29-12690 v83 a<p><span style="font-family:sans-serif; font-size:14.944px">We study the discrimination of von Neumann measurement in the scenario</span><span style="font-family:sans-serif; font-size:14.944px"> when we are given a reference measurement and some other measurement. The aim of</span><span style="font-family:sans-serif; font-size:14.944px"> the discrimination is to determine whether the other measurement is the same as the</span><span style="font-family:sans-serif; font-size:14.944px"> first one. We consider the cases when the reference measurement is given without the</span><span style="font-family:sans-serif; font-size:14.944px"> classical description and when its classical description is known. Both cases are studied</span><span style="font-family:sans-serif; font-size:14.944px"> in the symmetric and asymmetric discrimination setups. Moreover, we provide optimal</span><span style="font-family:sans-serif; font-size:14.944px"> certification schemes enabling us to certify a known quantum measurement against the</span><span style="font-family:sans-serif; font-size:14.944px"> unknown one.</span></p>
  a2521-327X00355nas a2200121   4500000000100000000000100001008004100002100002200043700002200065700002200087245007900109856004500188       2023                            d1 aFilip Maciejewski1 aZbigniew Puchała1 aMichał Oszmaniec00aExploring Quantum Average-Case Distances: Proofs, properties, and examples  uhttps://doi.org/10.1109/TIT.2023.325010000343nas a2200133   4500000000100000000000100001008004100002100002200043700002200065700002200087245004700109856004700156490000600203       2023                            d1 aFilip Maciejewski1 aZbigniew Puchała1 aMichał Oszmaniec00aOperational Quantum Average-Case Distances  uhttps://doi.org/10.22331/q-2023-09-11-11060 v701618nas a2200157   4500000000100000000000100001008004100002260001000043100003200053700002200085700001900107245002100126856004700147490000600194520126000200       2024                            d  c07/241 aHanna Wojewódka-Ściążko1 aZbigniew Puchała1 aKamil Korzekwa00aResource engines  uhttps://doi.org/10.22331/q-2024-01-10-12220 v83 a<p>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.</p>
02064nas a2200229   4500000000100000000000100001008004100002260001200043100002600055700002100081700001900102700001900121700002200140700002400162700002300186700002200209700002100231245008200252856002600334490000700360520146700367       2024                            d  c09/20141 aTomasz Śmierzchalski1 aJakub Pawłowski1 aArtur Przybysz1 aŁukasz Pawela1 aZbigniew Puchała1 aMátyás Koniorczyk1 aBartłomiej Gardas1 aSebastian Deffner1 aKrzysztof Domino00aHybrid quantum-classical computation for automatic guided vehicles scheduling  uhttps://rdcu.be/dUkwi0 v143 a<p>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.</p>
00633nas a2200229   4500000000100000000000100001008004100002100002300043700002300066700002500089700002200114700002300136700001900159700001800178700002400196700001700220700002500237700002200262700002100284700002200305245007600327       2023                            d1 aBartłomiej Gardas1 aPrzemysław Głomb1 aPrzemysław Sadowski1 aZbigniew Puchała1 aKonrad Jałowiecki1 aŁukasz Pawela1 aOrphee Faucoz1 aPierre-Marie Brunet1 aPiotr Gawron1 aMatthijs Van Waveren1 aMickaël Savinaud1 aGuillaume Pasero1 aVeronique Defonte00aHyper-Spectral Image Classification Using Adiabatic Quantum Computation00544nas a2200193   4500000000100000000000100001008004100002100002500043700002200068700002100090700002200111700002400133700001800157700001700175700002300192700002200215700001900237245009400256       2023                            d1 aMatthijs Van Waveren1 aMickaël Savinaud1 aGuillaume Pasero1 aVeronique Defonte1 aPierre-Marie Brunet1 aOrphee Faucoz1 aPiotr Gawron1 aBartłomiej Gardas1 aZbigniew Puchała1 aŁukasz Pawela00aComparison of Quantum Neural Network Algorithms For Earth Observation Data Classification00379nas a2200157   4500000000100000000000100001008004100002100002100043700002200064700001800086700001900104700002300123700002200146245004600168490000700214       2024                            d1 aRyszard Kukulski1 aMateusz Stępniak1 aKamil Hendzel1 aŁukasz Pawela1 aBartłomiej Gardas1 aZbigniew Puchała00aLocal certification of unitary operations0 v1400605nas a2200217   4500000000100000000000100001008004100002100001700043700002500060700002300085700002300108700002500131700002000156700002100176700002200197700002400219700001800243700002200261700001900283245008500302       2024                            d1 aPiotr Gawron1 aPrzemysław Sadowski1 aPrzemysław Głomb1 aBartłomiej Gardas1 aMatthijs Van Waveren1 aClément Forray1 aGuillaume Pasero1 aMickaël Savinaud1 aPierre-Marie Brunet1 aOrphee Faucoz1 aZbigniew Puchała1 aŁukasz Pawela00aWhat Could be Achieved with a Million Qubits Quantum Annealer in Remote Sensing?00694nas a2200145   4500000000100000000000100001008004100002100002200043700001900065700002200084245007100106856005500177520030200232022001400534       2026                            d1 aMarcin Markiewicz1 aŁukasz Pawela1 aZbigniew Puchała00aSingle-shot comparison of random quantum channels and measurements  uhttps://www.nature.com/articles/s41598-026-70695-z3 a<p>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.</p>
  a2045-232201509nas a2200145   4500000000100000000000100001008004100002260003800043100002200081700002100103700001900124245005000143520114900193022002101342       2025                            d  c05/2025aUnited States of America1 aZbigniew Puchała1 aRyszard Kukulski1 aŁukasz Pawela00aQuantum Probabilistic Error Correction Method3 a<p>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.</p>
  aUS 12,299,539 B201633nas a2200169   4500000000100000008004100001260001500042100001600057700002100073700002400094700001900118700002200137245012200159856003700281300000700318520113800325       2026                            d  c07/10/20261 aAdam Bílek1 aRyszard Kukulski1 aPaulina Lewandowska1 aŁukasz Pawela1 aZbigniew Puchała00aNoise Resilience of Quantum Key Distribution Protocols Secured Against Independent Attacks With One-Way Communication  uhttps://arxiv.org/abs/2607.11857  a193 aWe 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.01652nas a2200157   4500000000100000008004100001260001500042100002600057700001900083700002200102700002200124245007000146856003700216300000700253520123400260       2026                            d  c05/29/20261 aLudmiła Marcinkowska1 aŁukasz Pawela1 aMarcin Markiewicz1 aZbigniew Puchała00aAsymptotic distinguishability of Haar-averaged measurement models  uhttps://arxiv.org/abs/2605.31168  a493 aWe 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.01790nas a2200133   4500000000100000008004100001260001200042653010900054100001900163700002200182245008500204856003700289520133000326       2026                            d  c06/202610aSymbolic integration; Haar measure; Weingarten calculus; Julia programming language; quantum information1 aŁukasz Pawela1 aZbigniew Puchała00aIntegrateUnitary.jl: A Julia package for symbolic integration over Haar measures  uhttps://arxiv.org/abs/2605.238303 aSymbolic 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 > 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.02013nas a2200157   4500000000100000008004100001260001500042100002200057700001900079700002200098245009800120856003700218300000700255520155200262022004101814       2026                            d  c25/02/20261 aMarcin Markiewicz1 aŁukasz Pawela1 aZbigniew Puchała00aChoi-level twirling of quantum channels: finite constructions and non-compact transformations  uhttps://arxiv.org/abs/2512.23586  a153 a<p>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 <sup>in</sup>(U) = U <sup>⊗t</sup><sub><sup>in</sup></sub> and π <sup>out</sup>(U) = U <sup>⊗t</sup><sub><sup>out</sup></sub> , 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 <sup>⊗(t</sup><sub><sup>in</sup></sub><sup>+t</sup><sub><sup>out</sup></sub><sup>)</sup> , 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<sub>in</sub> + t<sub>out</sub>.</p>  a1751-8121 (online), 1751-8113 (druk)