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.01819nas a2200157   4500000000100000008004100001260001500042100002200057700001900079700002200098245009800120856003700218300000700255520135800262022004101620       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 aTwirling, 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 in(U) = U ⊗tin and π out(U) = U ⊗tout , 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 ⊗(tin+tout) , 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 = tin + tout.  a1751-8121 (online), 1751-8113 (druk)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.01493nas a2200133   4500000000100000008004100001260001500042100002100057700001900078700002000097245007100117856003700188520113400225       2026                            d  c09/03/20261 aLeonard Sikorski1 aŁukasz Pawela1 aKarol Horodecki00aLimitations on quantum key repeaters for all key correlated states  uhttps://arxiv.org/abs/2206.009933 aQuantum key repeater is the backbone of the future Quantum Internet. It is an open problem to determine, for an arbitrary mixed bipartite state shared between the stations of a quantum key repeater, how much key can be generated between its two end-nodes. We place a novel bound on the quantum key repeater rate, which uses the relative entropy distance from, in general, entangled quantum states. It allows us to generalize bounds on key repeaters of M. Christandl and R. Ferrara [Phys. Rev. Lett. 119, 220506]. As in the latter article, we consider a scenario used for measurement-device-independent quantum cryptography. The derived bound, although not tighter, holds for a more general class of states, thereby avoiding the NP-hard separability problem. We show that the repeated key of the broad class of key correlated states can exceed twice the one-way distillable entanglement by at most the max-relative entropy of entanglement of its attacked version. We also provide a non-trivial upper bound on the amount of private randomness of a generic independent bit — a state containing one bit of ideal private randomness.00431nas a2200157   4500000000100000008004100001260001500042100001800057700002100075700002000096700001900116700002300135245004100158856006600199490000800265       2026                            d  c29/04/20261 aJan Tuziemski1 aJakub Pawłowski1 aPaweł Tarasiuk1 aŁukasz Pawela1 aBartłomiej Gardas00aLimits of quantum run-time advantage  uhttps://journals.aps.org/prapplied/abstract/10.1103/gpsf-pn1x0 v 2500291nas a2200109   4500000000100000008004100001260001200042100001900054700002300073245007800096490000700174       2026                            d  c03/20261 aŁukasz Pawela1 aKarol Życzkowski00aMatrix logistic map: fractal spectral distributions and transfer of chaos0 v3601633nas 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.00517nas a2200145   4500000000100000008004100001100002300042700002100065700002300086700001900109245015000128856007200278490000700350022001400357       2026                            d1 aKonrad Jałowiecki1 aJakub Pawłowski1 aBartłomiej Gardas1 aŁukasz Pawela00aOmnisolver: An extensible interface to Ising spin–glass and QUBO solvers – a numerically stabilized, distributed GPU exhaustive-search plugin  uhttps://www.sciencedirect.com/science/article/pii/S23527110260052240 v36  a2352-711001981nas a2200121   4500000000100000008004100001260001500042100001900057245004900076856003700125300000700162520169000169       2026                            d  c01/02/20261 aŁukasz Pawela00aParrondo paradox in quantum image encryption  uhttps://arxiv.org/abs/2508.16382  a103 aWe present a quantum image encryption protocol that harnesses discrete-time quantum walks (DTQWs) on cycles and explicitly examines the role of the Parrondo paradox in security. Using the NEQR representation, a DTQW-generated probability mask is transformed into a quantum key image and applied via CNOT to encrypt grayscale images. We adopt an efficient circuit realization of DTQWs based on QFT-diagonalization and coin-conditioned phase layers, yielding low depth for N = 2^n positions and t steps. On 64 × 64 benchmark images, the scheme suppresses adjacent-pixel correlations to near zero after encryption (e.g., |C_H|, |C_V|, |C_D| ≈ 10⁻²), produces nearly uniform histograms, and achieves high ciphertext entropy close to the 8-bit ideal. Differential analyses further indicate strong diffusion and confusion: NPCR exceeds 99% and UACI is around 30%, consistent with robust sensitivity to small plaintext changes. Crucially, we investigate the impact of the Parrondo paradox on encryption quality and demonstrate that our fully unitary protocol remains robust even in paradoxical regimes. We show that while the paradox can introduce biases in simpler measurement-based schemes, our integrated approach which incorporates spatial diffusion and position-color entanglement, effectively leverages the complex interference patterns of the Parrondo walk to enhance substitution, maintaining high entropy and low correlations. Our results provide a performant DTQW-based quantum image cipher and confirm the suitability of paradoxical dynamics for secure quantum image processing. We discuss implications for hardware implementations and extensions to higher-dimensional walks.00359nas a2200133   4500000000100000008004100001100002000042700002000062700001800082700001900100700002300119245004400142856003900186       2026                            d1 aJakub Pawlowski1 aPaweł Tarasiuk1 aJan Tuziemski1 aŁukasz Pawela1 aBartłomiej Gardas00aSimulated Bifurcation Quantum Annealing  uhttps://arxiv.org/abs/2604.01050v100672nas a2200133   4500000000100000008004100001100002200042700001900064700002200083245007100105856005500176520029300231022001400524       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 aIn 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.  a2045-232200453nas a2200157   4500000000100000008004100001260001600042100002000058700001900078700001800097700001900115700002300134245006500157856006600222490000700288       2026                            d  c 08/07/20261 aJakub Pawlowski1 aPawel Tarasiuk1 aJan Tuziemski1 aŁukasz Pawela1 aBartłomiej Gardas00aToward quantum scaling advantage in approximate optimization  uhttps://journals.aps.org/prapplied/abstract/10.1103/qcws-8kgm0 v2600420nas a2200121   4500000000100000008004100001100001900042700002300061245012100084856007200205490000700277022001400284       2026                            d1 aŁukasz Pawela1 aBartłomiej Gardas00aVersion 2.0.1 - SpinGlassPEPS.jl: Tensor-network package for Ising-like optimization on quasi-two-dimensional graphs  uhttps://www.sciencedirect.com/science/article/pii/S23527110260051820 v36  a2352-711000403nas a2200157   4500000000100000008004100001100002100042700001800063700002000081700001900101700001900120700001800139700001900157700002300176245004600199       2025                            d1 aJakub Pawłowski1 aJan Tuziemski1 aPaweł Tarasiuk1 aArtur Przybysz1 aRobert Adamski1 aKamil Hendzel1 aŁukasz Pawela1 aBartłomiej Gardas00a VeloxQ: A Fast and Efficient QUBO Solver01487nas a2200133   4500000000100000008004100001260003800042100002200080700002100102700001900123245005000142520114000192022002101332       2025                            d  c05/2025aUnited States of America1 aZbigniew Puchała1 aRyszard Kukulski1 aŁukasz Pawela00aQuantum Probabilistic Error Correction Method3 aA 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.  aUS 12,299,539 B201918nas a2200145   4500000000100000008004100001100002400042700002400066700002300090700002000113700001900133245006100152856006700213520149200280       2025                            d1 aPrzemysław Sekuła1 aMichał Romaszewski1 aPrzemysław Głomb1 aMichał Cholewa1 aŁukasz Pawela00aQuantum-aware Transformer model for state classification  uhttps://link.springer.com/chapter/10.1007/978-3-031-97570-7_153 aEntanglement is a fundamental feature of quantum mechanics, playing a crucial role in quantum information processing. However, classifying entangled states, particularly in the mixed-state regime, remains a challenging problem, especially as system dimensions increase. In this work, we focus on bipartite quantum states and present a data-driven approach to entanglement classification using transformer-based neural networks. Our dataset consists of a diverse set of bipartite states, including pure separable states, Werner entangled states, general entangled states, and maximally entangled states. We pretrain the transformer in an unsupervised fashion by masking elements of vectorized Hermitian matrix representations of quantum states, allowing the model to learn structural properties of quantum density matrices. This approach enables the model to generalize entanglement characteristics across different classes of states. Once trained, our method achieves near-perfect classification accuracy, effectively distinguishing between separable and entangled states. Compared to previous Machine Learning, our method successfully adapts transformers for quantum state analysis, demonstrating their ability to systematically identify entanglement in bipartite systems. These results highlight the potential of modern machine learning techniques in automating entanglement detection and classification, bridging the gap between quantum information theory and artificial intelligence.01444nas a2200193   4500000000100000008004100001100002600042700001800068700002300086700002100109700001900130700002300149700001500172245010500187856007200292490000700364520086500371022001401236       2025                            d1 aTomasz Śmierzchalski1 aAnna Dziubyna1 aKonrad Jałowiecki1 aZakaria Mzaouali1 aŁukasz Pawela1 aBartłomiej Gardas1 aMarek Rams00aSpinGlassPEPS.jl: Tensor-network package for Ising-like optimization on quasi-two-dimensional graphs  uhttps://www.sciencedirect.com/science/article/pii/S23527110250022490 v313 aThis work introduces SpinGlassPEPS.jl, a software package implemented in Julia, designed to find low-energy configurations of generalized Potts models, including Ising and QUBO problems, utilizing heuristic tensor network contraction algorithms on quasi-2D geometries. In particular, the package employs the Projected Entangled-Pairs States to approximate the Boltzmann distribution corresponding to the model’s cost function. This enables an efficient branch-and-bound search (within the probability space) that exploits the locality of the underlying problem’s topology. As a result, our software enables the discovery of low-energy configurations for problems on quasi-2D graphs, particularly those relevant to modern quantum annealing devices. The modular architecture of SpinGlassPEPS.jl supports various contraction schemes and hardware acceleration.  a2352-711001009nas a2200157   4500000000100000008004100001260001200042100002300054700001900077700002200096245006900118856004700187490000600234520059700240022001400837       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 aWe study the discrimination of von Neumann measurement in the scenario when we are given a reference measurement and some other measurement. The aim of the discrimination is to determine whether the other measurement is the same as the first one. We consider the cases when the reference measurement is given without the classical description and when its classical description is known. Both cases are studied in the symmetric and asymmetric discrimination setups. Moreover, we provide optimal certification schemes enabling us to certify a known quantum measurement against the unknown one.  a2521-327X02042nas a2200217   4500000000100000008004100001260001200042100002600054700002100080700001900101700001900120700002200139700002400161700002300185700002200208700002100230245008200251856002600333490000700359520145800366       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 aMotivated 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.00366nas a2200145   4500000000100000008004100001100002100042700002200063700001800085700001900103700002300122700002200145245004600167490000700213       2024                            d1 aRyszard Kukulski1 aMateusz Stępniak1 aKamil Hendzel1 aŁukasz Pawela1 aBartłomiej Gardas1 aZbigniew Puchała00aLocal certification of unitary operations0 v1400378nas a2200145   4500000000100000008004100001100002300042700002200065700002100087700001900108700001900127245004300146856003700189490000600226       2024                            d1 aFereshte Shahbeigi1 aChristopher Chubb1 aRyszard Kukulski1 aŁukasz Pawela1 aKamil Korzekwa00aQuantum-embeddable stochastic matrices  uhttps://arxiv.org/abs/2305.171630 v800592nas a2200205   4500000000100000008004100001100001700042700002500059700002300084700002300107700002500130700002000155700002100175700002200196700002400218700001800242700002200260700001900282245008500301       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?00531nas a2200181   4500000000100000008004100001100002500042700002200067700002100089700002200110700002400132700001800156700001700174700002300191700002200214700001900236245009400255       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 Classification00620nas a2200217   4500000000100000008004100001100002300042700002300065700002500088700002200113700002300135700001900158700001800177700002400195700001700219700002500236700002200261700002100283700002200304245007600326       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 Computation00341nas a2200109   4500000000100000008004100001100002300042700001900065245006800084856007200152490000700224       2023                            d1 aKonrad Jałowiecki1 aŁukasz Pawela00aOmnisolver: an extensible interface to Ising spin glass solvers  uhttps://www.softxjournal.com/article/S2352-7110(23)00255-8/fulltext0 v2400370nas a2200145   4500000000100000008004100001260001200042100002100054700001900075700002200094245005000116856003700166490000700203022001400210       2023                            d  c07/20231 aRyszard Kukulski1 aŁukasz Pawela1 aZbigniew Puchała00aOn the probabilistic quantum error correction  uhttps://arxiv.org/abs/2206.052320 v69  a1557-965400351nas a2200121   4500000000100000008004100001100002300042700002400065700001900089245007700108856003700185490000700222       2023                            d1 aKonrad Jałowiecki1 aPaulina Lewandowska1 aŁukasz Pawela00aPyQBench: a Python library for benchmarking gate-based quantum computers  uhttps://arxiv.org/abs/2304.000450 v2400373nas a2200133   4500000000100000008004100001260001200042100002400054700001900078700002200097245006600119856004700185490000700232       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 v1300466nas a2200145   4500000000100000008004100001260001200042100002600054700001900080700002200099700002200121700002300143245008700166856006700253       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_2200385nas a2200145   4500000000100000008004100001260001200042100002400054700002100078700001900099700002200118245005400140856003700194490000800231       2022                            d  c10/20221 aPaulina Lewandowska1 aRyszard Kukulski1 aŁukasz Pawela1 aZbigniew Puchała00aStorage and retrieval of von Neumann measurements  uhttps://arxiv.org/abs/2204.030290 v10600384nas a2200133   4500000000100000008004100001100001400042700002300056700001900079245006200098856006200160490000700222022002100229       2021                            d1 aAdam Glos1 aAleksandra Krawiec1 aŁukasz Pawela00aAsymptotic entropy of the Gibbs state of complex networks  uhttps://www.nature.com/articles/s41598-020-78626-2#citeas0 v11  aarXiv:2003.0841100390nas a2200133   4500000000100000008004100001260001200042100002300054700001900077700002200096245007200118856005900190490000700249       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 v1100396nas a2200157   4500000000100000008004100001260001200042100002100054700001600075700001900091700002200110700002200132245003900154856003800193490000700231       2021                            d  c07/20211 aRyszard Kukulski1 aIon Nechita1 aŁukasz Pawela1 aZbigniew Puchała1 aKarol Życzkowski00aGenerating random quantum channels  uhttps://doi.org/10.1063/5.00388380 v6201476nas a2200157   4500000000100000008004100001100002200042700001900064700002300083700002100106700002200127245007700149856006100226490000600287520102500293       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 aWe 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.01299nas a2200145   4500000000100000008004100001100002400042700002300066700002100089700001900110700002200129245006100151490000700212520093400219       2021                            d1 aPaulina Lewandowska1 aAleksandra Krawiec1 aRyszard Kukulski1 aŁukasz Pawela1 aZbigniew Puchała00aOn the optimal certification of von Neumann measurements0 v113 aCertification 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 q-numerical range.00262nas a2200109   4500000000100000008004100001100001900042700001900061700002200080245004300102490000700145       2021                            d1 aDariusz Kurzyk1 aŁukasz Pawela1 aZbigniew Puchała00aRelating entropies of quantum channels0 v2300273nas a2200109   4500000000100000008004100001100002300042700001900065700002200084245005000106490000700156       2020                            d1 aAleksandra Krawiec1 aŁukasz Pawela1 aZbigniew Puchała00aDiscrimination of POVMs with rank-one effects0 v1900641nas a2200121   4500000000100000008004100001100002400042700002100066700001900087245004700106856003700153520032900190       2020                            d1 aPaulina Lewandowska1 aRyszard Kukulski1 aŁukasz Pawela00aOptimal representation of quantum channels  uhttps://arxiv.org/abs/2002.055073 aThis work shows an approach to reduce the dimensionality of matrix representations of quantum channels. It is achieved by finding a base of the cone of positive semidefinite matrices which represent quantum channels. Next, this is implemented in the Julia programming language as a part of the QuantumInformation.jl package.00789nas a2200121   4500000000100000008004100001100002100042700002400063700001900087245006000106856003700166520046400203       2020                            d1 aRyszard Kukulski1 aPaulina Lewandowska1 aŁukasz Pawela00aPerturbation of the numerical range of unitary matrices  uhttps://arxiv.org/abs/2002.055533 aIn this work we show how to approach the problem of manimulating the numerical range of a unitary matrix. This task has farreaching impact on the study of discrimination of quantum measurements. We achieve the aforementioned manipulation by introducing a method which allows us to find a unitary matrix whose numerical range contains the origin where at the same time the distance between unitary matrix and its perturbation is relative small in given metric.00314nas a2200133   4500000000100000008004100001260000900042100002500051700001900076700002400095700002100119245003300140490000700173       2019                            d  c20191 aPrzemysław Sadowski1 aŁukasz Pawela1 aPaulina Lewandowska1 aRyszard Kukulski00aQuantum walks on hypergraphs0 v5801216nas a2200157   4500000000100000008004100001100001600042700002200058700001900080700002200099245004800121856003800169300001100207490000700218520083300225       2018                            d1 aIon Nechita1 aZbigniew Puchała1 aŁukasz Pawela1 aKarol Życzkowski00aAlmost all quantum channels are equidistant  uhttps://doi.org/10.1063/1.5019322  a0522010 v593 aIn 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 1/2+2/π. Furthermore, we show that for a random state ρ 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 ρ may be interpreted as a Jamio{\l}kowski state of a unital map.01028nas a2200145   4500000000100000008004100001100001900042700001900061700002200080245006900102856004600171300000800217490000700225520065000232       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 aThe 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.01019nas a2200145   4500000000100000008004100001100002100042700001700063700001900080245005900099856005400158300001000212490000700222520064400229       2018                            d1 aKrzysztof Domino1 aPiotr Gawron1 aŁukasz Pawela00aEfficient computation of higher order cumulant tensors  uhttps://epubs.siam.org/doi/abs/10.1137/17M1149365  aA16100 v403 aIn this paper, we introduce a novel algorithm for calculating arbitrary order cumulants of multidimensional data. Since the d'th order cumulant can be presented in the form of an d-dimensional tensor, the algorithm is presented using tensor operations. The algorithm provided in the paper takes advantage of super-symmetry of cumulant and moment tensors. We show that the proposed algorithm considerably reduces the computational complexity and the computational memory requirement of cumulant calculation as compared with existing algorithms. For the sizes of interest, the reduction is of the order of d! compared to the naive algorithm.00417nas a2200145   4500000000100000008004100001100002100042700001400063700002400077700001900101700002500120245008000145856003900225490000700264       2018                            d1 aKrzysztof Domino1 aAdam Glos1 aMateusz Ostaszewski1 aŁukasz Pawela1 aPrzemysław Sadowski00aProperties of quantum stochastic walks from the asymptotic scaling exponent  uhttps://doi.org/10.26421/QIC18.3-40 v1800399nas a2200133   4500000000100000008004100001260001200042100001700054700001900071700001900090245010000109856004900209490000700258       2018                            d  c12/20181 aPiotr Gawron1 aDariusz Kurzyk1 aŁukasz Pawela00aQuantumInformation.jl—a Julia package for numerical computation in quantum information theory  uhttps://doi.org/10.1371/journal.pone.02093580 v1301695nas a2200145   4500000000100000008004100001100002200042700001900064700002300083700002100106245007800127856003700205490000700242520130000249       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 aIn 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.00891nas a2200145   4500000000100000008004100001100001900042700001900061700002200080245007400102856004600176300000800222490000700230520050800237       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 aQuantum 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.00266nas a2200097   4500000000100000008004100001100002500042700001900067245007500086490000700161       2016                            d1 aPrzemysław Sadowski1 aŁukasz Pawela00aCentral limit theorem for reducible and irreducible open quantum walks0 v1500422nas a2200157   4500000000100000008004100001100001400042700001800056700001900074700001100093700002100104700001900125700002500144245008800169490000700257       2016                            d1 aAndy Chia1 aAnna Górecka1 aŁukasz Pawela1 aK. Tan1 aPiotr Kurzyński1 aTomasz Paterek1 aDagomir Kaszlikowski00aCoherent chemical kinetics as quantum walks I: Reaction operators for radical pairs0 v9301193nas a2200133   4500000000100000008004100001100002200042700001900064700002200083245004900105856004700154490000700201520085100208       2016                            d1 aZbigniew Puchała1 aŁukasz Pawela1 aKarol Życzkowski00aDistinguishability of generic quantum states  uhttps://doi.org/10.1103/PhysRevA.93.0621120 v933 aProperties 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 =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.00746nas a2200121   4500000000100000008004100001100001900042700002200061245008000083856004600163490000700209520040800216       2016                            d1 aŁukasz Pawela1 aZbigniew Puchała00aQuantifying channels output similarity with applications to quantum control  uhttps://doi.org/10.1007/s11128-015-1238-z0 v153 aIn 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.00227nas a2200097   4500000000100000008004100001100001900042245004600061300001400107490000800121       2016                            d1 aŁukasz Pawela00aQuantum games on evolving random networks  a179–1880 v45800283nas a2200121   4500000000100000008004100001100001700042700001900059245004200078300000900120490000700129022002500136       2016                            d1 aPiotr Gawron1 aŁukasz Pawela00aRelativistic Quantum Pseudo-telepathy  a11470 v47  a0587-4254, 1509-577000303nas a2200109   4500000000100000008004100001100001900042700002500061245008600086490000700172022001400179       2016                            d1 aŁukasz Pawela1 aPrzemysław Sadowski00aVarious methods of optimizing control pulses for quantum systems with decoherence0 v15  a1310.210900337nas a2200133   4500000000100000008004100001100001900042700001700061700002200078700002500100245005800125300001300183490000700196       2015                            d1 aŁukasz Pawela1 aPiotr Gawron1 aJaroslaw Miszczak1 aPrzemysław Sadowski00aGeneralized open quantum walks on Apollonian networks  ae01309670 v1000353nas a2200121   4500000000100000008004100001100001900042700002200061245008100083856004600164300001400210490000700224       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 v1400448nas a2200169   4500000000100000008004100001100001800042700001700060700001900077700002200096700002200118245005200140856004600192300001200238490000800250520002000258       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 aarXiv:1409.494100377nas a2200145   4500000000100000008004100001100001700042700001900059700002200078700002000100700002200120245006800142300001400210490000700224       2015                            d1 aPiotr Gawron1 aŁukasz Pawela1 aZbigniew Puchała1 aJacek Szklarski1 aKarol Życzkowski00aWybory samorządowe 2014 w poszukiwaniu anomalii statystycznych  a534–5450 v3000299nas a2200109   4500000000100000008004100001100001700042700001900059700001900078245008500097490000700182       2014                            d1 aPiotr Gawron1 aDariusz Kurzyk1 aŁukasz Pawela00aDecoherence effects in the quantum qubit flip game using Markovian approximation0 v1300317nas a2200109   4500000000100000008004100001100002200042700001900064700002000083245009700103490000700200       2014                            d1 aJaroslaw Miszczak1 aŁukasz Pawela1 aJan Sładkowski00aGeneral model for a entanglement-enhanced composed quantum game on a two-dimensional lattice0 v1301234nas a2200133   4500000000100000008004100001100001900042700002200061245004600083856004600129300001400175490000700189520090400196       2014                            d1 aŁukasz Pawela1 aZbigniew Puchała00aQuantum control with spectral constraints  uhttps://doi.org/10.1007/s11128-013-0644-3  a227–2370 v133 aVarious 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.00415nas a2200157   4500000000100000008004100001100002300042700001700065700002200082700001900104700002200123245007900145300001200224490000700236022001400243       2013                            d1 aRyszard Winiarczyk1 aPiotr Gawron1 aJaroslaw Miszczak1 aŁukasz Pawela1 aZbigniew Puchała00aAnalysis of patent activity in the field of quantum information processing  a13500070 v11  a0219-749900252nas a2200109   4500000000100000008004100001100001900042700002000061245004100081300001200122490000800134       2013                            d1 aŁukasz Pawela1 aJan Sładkowski00aCooperative quantum Parrondo's games  a51–570 v25600327nas a2200133   4500000000100000008004100001100001900042700001700061700002200078700002000100245005600120300001100176490000600187       2013                            d1 aŁukasz Pawela1 aPiotr Gawron1 aZbigniew Puchała1 aJan Sładkowski00aEnhancing pseudo-telepathy in the Magic Square game  ae646940 v800272nas a2200109   4500000000100000008004100001100001900042700002000061245005900081300001400140490000800154       2013                            d1 aŁukasz Pawela1 aJan Sładkowski00aQuantum Prisoner's Dilemma game on hypergraph networks  a910–9170 v39200263nas a2200109   4500000000100000008004100001100001900042245005700061300001400118490000700132022001400139       2011                            d1 aŁukasz Pawela00aControl parameters for the quantum Deutsch algorithm  a193–2000 v23  a1896-533400451nas a2200157   4500000000100000008004100001100002000042700001300062700001300075700001300088700001900101700001400120245013700134300001400271490000800285       2011                            d1 aP. Kościelniak1 aJ. Mazur1 aJ. Henek1 aM. Kwoka1 aŁukasz Pawela1 aJ. Szuber00aXPS and AFM studies of surface chemistry and morphology of In2O3 ultrathin films deposited by rheotaxial growth and vacuum oxidation  a927–9310 v52000388nas a2200145   4500000000100000008004100001100002300042700001900065700001700084700001900101700001900120245008400139300001100223490000800234       2010                            d1 aTomasz Błachowicz1 aAndrea Ehrmann1 aA. Tillmanns1 aP. Stebliński1 aŁukasz Pawela00aMagnetization reversal in magnetic half-balls influenced by shape perturbations  a1239060 v10800313nas a2200121   4500000000100000008004100001100001700042700001300059700002300072700001900095700001900114245005800133       2010                            d1 aA. Tillmanns1 aM. Weber1 aTomasz Błachowicz1 aŁukasz Pawela1 aT. Kammermeier00aTextile Magnets as Base for Micromagnetic Simulations