arXiv subjects

Paulina Lewandowska

Publications and source records attributed to Paulina Lewandowska.

15 recordsLinked to original sources

arXiv2026

Parallel quantum channel discrimination and numerical ranges in tensor product subspaces

Quantum channel discrimination plays a crucial role in quantum information theory. Of particular interest is the case in which the channels can be discriminated perfectly. In this work, we focus on the perfect quantum channel discrimination task in a parallel scheme. We develop an SDP formulation combined with a bisection procedure to compute a quantum state for perfect discrimination in time linear in the number of copies. In addition, we obtain the minimal number of copies of quantum channels to achieve perfect discrimination. Thanks to that, we settle in the affirmative Conjecture 1 of Duan, Guo, Li and Li [arXiv:1605.02294, IEEE ISIT 2016], which characterizes the number of parallel uses needed to discriminate perfectly a distinguished family of operator subspaces. All our results are obtained using the notion and basic properties of the numerical range. In particular, the key fact that we prove and use is that the minimal angle of the numerical range of a tensor product of matrix subspaces equals the sum of the minimal angles of the numerical ranges of the individual subspaces.

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arXiv2026

Noise Resilience of Quantum Key Distribution Protocols Secured Against Independent Attacks With One-Way Communication

We investigate the resilience to noise of single-qubit quantum key distribution (QKD) protocols in the scenario of security against independent eavesdropping attacks and key distillation based on one-way classical communication. To this end, we introduce a noise-based metric that quantifies the efficiency of QKD protocols. Within this framework, we analyze the maximal noise levels that allow Alice and Bob to asymptotically establish a secure secret key. Using this assumption, we compare the noise tolerance of general single-qubit QKD protocols, in particular the BB84, B92, E91, and six-state protocols. Our main result determines the noise level threshold for QKD allowing one to distill an asymptotically secure secret key. Additionally, we demonstrate that the six-state protocol achieves the greatest resistance to noise while simultaneously yielding a higher post-selection efficiency than the other analyzed single-qubit protocols, confirming its robustness within the considered security model. Finally, we perform an analysis of the proposed noise-based metric and the conventional quantum bit error rate (QBER) metric.

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arXiv2026

Resource-Efficient Variational Quantum Classifier

We introduce the unambiguous quantum classifier based on Hamming distance measurements combined with classical post-processing. The proposed approach improves classification performance through a more effective use of ansatz expressivity, while requiring significantly fewer circuit evaluations. Moreover, the method demonstrates enhanced robustness to noise, which is crucial for near-term quantum devices. We evaluate the proposed method on a breast cancer classification dataset. The unambiguous classifier achieves an average accuracy of 90%, corresponding to an improvement of 6.9 percentage points over the baseline, while requiring eight times fewer circuit executions per prediction. In the presence of noise, the improvement is reduced to approximately 3.1 percentage points, with the same reduction in execution cost. We substantiate our experimental results with theoretical evidence supporting the practical performance of the approach.

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arXiv2026

A Bipartite Quantum Key Distribution Protocol Based on Indefinite Causal Order

We propose a bipartite quantum key distribution (QKD) protocol based on causal nonseparability: the presence of a resource -- a process matrix -- that does not correspond to any definite causal order between two parties. In our protocol, Alice and Bob perform local operations arranged in a ``causal-order guessing game,'' whereby each round yields an 85.35\% probability of matching bits when the communication is undisturbed. This raw matching probability (or equivalently, a $\sim14.65\%$ error rate) is amenable to standard forward error-correction strategies. We further discuss the practical construction of the QKD protocol using indefinite causal order, where several different scenarios are deeply analyzed.

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arXiv2025

Benchmarking gate-based quantum devices via certification of qubit von Neumann measurements

We present an updated version of PyQBench, an open-source Python library designed for benchmarking gate-based quantum computers, with a focus on certifying qubit von Neumann measurements. This version extends PyQBench's capabilities by incorporating a certification scheme of quantum measurements that evaluates the accuracy on Noisy Intermediate-Scale Quantum devices, alongside its original functionality of von Neumann measurements' discrimination. PyQBench offers a user-friendly command-line interface and Python library integration, allowing users to implement custom measurement schemes and error models for more advanced benchmarking tasks. The new version is specifically designed to support IBM Q devices through integration with the Qiskit library, enabling seamless benchmarking on real quantum hardware. By providing flexible benchmarking tools, PyQBench addresses the critical need for reliable performance metrics in the NISQ era, contributing to the development of error mitigation techniques and the verification of quantum measurement fidelity. The source code is available on GitHub under an open-source license, encouraging community collaboration and further advancements in quantum hardware benchmarking.

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arXiv2025

Experimental study of multiple-shot unitary channels discrimination using the IBM Q computers

Tasks involving black boxes appear frequently in quantum computer science. An example that has been deeply studied is quantum channel discrimination. In this work, we study the discrimination between two quantum unitary channels in the multiple-shot scenario. We challenge the theoretical results concerning the probability of correct discrimination with the results collected from experiments performed on the IBM Quantum processor Brisbane. Our analysis shows that neither too deep quantum circuits nor circuits that create too much entanglement are suitable for the discrimination task. We conclude that circuit architectures which minimize entanglement overhead while preserving discrimination power are significantly more resilient to hardware noise if their depth does not overpass threshold value.

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arXiv2024

Shared entanglement for three-party causal order guessing game

In a variant of communication tasks, players cooperate in choosing their local strategies to compute a given task later, working separately. Utilizing quantum bits for communication and sharing entanglement between parties is a recognized method to enhance performance in these situations. In this work, we introduce the game for which three parties, Alice, Bob and Charlie, would like to discover the hidden order in which they make the moves. We show the advantage of quantum strategies that use shared entanglement and local operations over classical setups for discriminating operations' composition order. The role of quantum resources improving the probability of successful discrimination is also investigated.

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arXiv2024

Storage and retrieval of von Neumann measurements via indefinite causal order structures

This work presents the problem of learning an unknown von Neumann measurement of dimension $d$ using indefinite causal structures. In the considered scenario, we have access to $N$ copies of the measurement. We use formalism of process matrices to store information about the given measurement, that later will be used to reproduce its best possible approximation. Our goal is to compute the maximum value of the average fidelity function $F_d(N)$ of our procedure. We prove that $F_d(N) = 1 - Θ\left( \frac{1}{N^2}\right)$ for arbitrary but fixed dimension $d$. Furthermore, we present the SDP program for computing $F_d(N)$. Basing on the numerical investigation, we show that for the qubit von Neumann measurements using indefinite causal learning structures provide better approximation than quantum networks, starting from $N \ge 3$.

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arXiv2023

PyQBench: a Python library for benchmarking gate-based quantum computers

We introduce PyQBench, an innovative open-source framework for benchmarking gate-based quantum computers. PyQBench can benchmark NISQ devices by verifying their capability of discriminating between two von Neumann measurements. PyQBench offers a simplified, ready-to-use, command line interface (CLI) for running benchmarks using a predefined parametrized Fourier family of measurements. For more advanced scenarios, PyQBench offers a way of employing user-defined measurements instead of predefined ones.

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arXiv2022

Storage and retrieval of von Neumann measurements

This work examines the problem of learning an unknown von Neumann measurement of dimension $d$ from a finite number of copies. To obtain a faithful approximation of the given measurement we are allowed to use it $N$ times. Our main goal is to estimate the asymptotic behavior of the maximum value of the average fidelity function $F_d$ for a general $N \rightarrow 1$ learning scheme. We show that $F_d = 1 - Θ\left(\frac{1}{N^2}\right)$ for arbitrary but fixed dimension $d$. In addition to that, we compared various learning schemes for $d=2$. We observed that the learning scheme based on deterministic port-based teleportation is asymptotically optimal but performs poorly for low $N$. In particular, we discovered a parallel learning scheme, which despite its lack of asymptotic optimality, provides a high value of the fidelity for low values of $N$ and uses only two-qubit entangled memory states.

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arXiv2022

Strategies for single-shot discrimination of process matrices

The topic of causality has recently gained traction quantum information research. This work examines the problem of single-shot discrimination between process matrices which are an universal method defining a causal structure. We provide an exact expression for the optimal probability of correct distinction. In addition, we present an alternative way to achieve this expression by using the convex cone structure theory. We also express the discrimination task as semidefinite programming. Due to that, we have created the SDP calculating the distance between process matrices and we quantify it in terms of the trace norm. As a valuable by-product, the program finds an optimal realization of the discrimination task. We also find two classes of process matrices which can be distinguished perfectly. Our main result, however, is a consideration of the discrimination task for process matrices corresponding to quantum combs. We study which strategy, adaptive or non-signalling, should be used during the discrimination task. We proved that no matter which strategy you choose, the probability of distinguishing two process matrices being a quantum comb is the same.

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arXiv2020

On the optimal certification of von Neumann measurements

In this report we study certification of quantum measurements, which can be viewed as the extension of quantum hypotheses testing. This extension involves also the study of the input state and the measurement procedure. Here, we will be interested in two-point (binary) certification scheme in which the null and alternative hypotheses are single element sets. Our goal is to minimize the probability of the type II error given some fixed statistical significance. 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. From our main result follow the conditions when two pure states, unitary operations and von Neumann measurements cannot be distinguished perfectly but still can be certified with a given statistical significance. Moreover, we show the connection between the certification of quantum channels or von Neumann measurements and the notion of $q$-numerical range.

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arXiv2020

Optimal representation of quantum channels

This 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.

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arXiv2020

Perturbation of the numerical range of unitary matrices

In this work we show how to approach the problem of manimulating the numerical range of a unitary matrix. This task has far-reaching 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.

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arXiv2019

Quantum walks on hypergraphs

In this work we introduce the concept of a quantum walk on a hypergraph. We show that the staggered quantum walk model is a special case of a quantum walk on a hypergraph.

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