arXiv subjects

Piotr Masajada

Publications and source records attributed to Piotr Masajada.

4 recordsLinked to original sources

arXiv2026

Asymptotic Limits of Entanglement Transmission

Reliable distribution of quantum entanglement over long distances is a central challenge in quantum information science, fundamentally limited by decoherence in noisy communication channels. In this work, we investigate the asymptotic limits of entanglement distribution across homogeneous linear repeater chains with arbitrary intermediate LOCC processing. We establish a strict dichotomy: the asymptotic preservation of entanglement over arbitrarily long distances is possible if and only if the underlying quantum channel admits a correctable subspace. For channels lacking such a subspace, we prove that the transmitted state converges exponentially fast to the set of separable states, rendering standard LOCC filtering insufficient. To counteract this exponential degradation, we analyze ``networks'' employing parallel channel uses per link. We derive a fundamental lower bound on the required number of parallel channel uses per elementary link, proving that for broad classes of channels without a correctable subspace, the number of parallel channels per link must scale at least logarithmically with the number of intermediate stations to sustain a non-zero amount of entanglement. This provides a code-independent bound for the number of physical links for the considered homogeneous one-way architecture. For depolarizing noise below the corresponding coding threshold, the logarithmic lower bound is achievable.

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arXiv2025

ENTCALC: Toolkit for calculating geometric entanglement in multipartite quantum systems

We present entcalc, a Python and MATLAB package for estimating the geometric entanglement of multipartite quantum states. The package operates as follows: given a multipartite quantum state as input, it outputs an estimate of its geometric entanglement. For pure states, it computes the geometric entanglement together with an estimation error. For mixed states, it provides both lower and upper bounds on the geometric entanglement, thereby identifying an interval in which the true value lies. We provide several methods to compute the lower bound, enabling users to balance accuracy against computational cost. We apply entcalc to several representative examples, including for $3\otimes3$ PPT entangled states, mixtures of GHZ and W states, thermal states of selected three-qubit spin chains, and noisy GHZ and W states. We observe signatures of quantum phase transitions by quantifying entanglement in spin chains. We also demonstrate that entanglement between non-neighbouring sites can be activated by tuning the external magnetic field. In all tested cases, the gap between the lower and upper bounds is found to be very small, indicating that entcalc provides highly accurate estimates of the geometric entanglement for these states.

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arXiv2025

Optimizing entanglement distribution via noisy quantum channels

Entanglement distribution is a crucial problem in quantum information science, owing to the essential role that entanglement plays in enabling advanced quantum protocols, including quantum teleportation and quantum cryptography. We investigate strategies for distributing quantum entanglement between two distant parties through noisy quantum channels. Specifically, we compare two configurations: one where the entanglement source is placed at the midpoint of the communication line, and another where it is located at one end. For certain families of qubit channels we show analytically that the midpoint strategy is optimal. Based on extensive numerical analysis, we conjecture that this strategy is generally optimal for all qubit channels. Focusing on the midpoint configuration, we develop semidefinite programming (SDP) techniques to assess whether entanglement can be successfully distributed through the network, and to quantify the amount of entanglement that can be distributed in the process. In many relevant cases the SDP formulation reliably captures the maximal amount of entanglement which can be distributed, if entanglement is quantified using the negativity. We analyze several channel models and demonstrate that, for various combinations of amplitude damping and depolarizing noise, entanglement distribution is only possible with weakly entangled input states. Excessive entanglement in the input state can hinder the channel's ability to establish entanglement. Our findings have implications for optimizing entanglement distribution in realistic quantum communication networks.

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arXiv2025

Local Purity Distillation in Quantum Systems: Exploring the Complementarity Between Purity and Entanglement

Quantum thermodynamics and quantum entanglement represent two pivotal quantum resource theories with significant relevance in quantum information science. Despite their importance, the intricate relationship between these two theories is still not fully understood. Here, we delve into the interplay between entanglement and thermodynamics, particularly in the context of local cooling processes. We introduce and develop the framework of Gibbs-preserving local operations and classical communication. Within this framework, we explore strategies enabling remote parties to effectively cool their local systems to the ground state. Our analysis is centered on scenarios where only a single copy of a quantum state is accessible, with the ideal performance defined by the highest possible fidelity to the ground state achievable under these constraints. We focus on systems with fully degenerate local Hamiltonians, where local cooling aligns with the extraction of local purity. In this context, we establish a powerful link between the efficiency of local purity extraction and the degree of entanglement present in the system, a concept we define as purity-entanglement complementarity. Moreover, we demonstrate that in many pertinent scenarios, the optimal performance can be precisely determined through semidefinite programming techniques. Our findings open doors to various practical applications, including techniques for entanglement detection and estimation. We demonstrate this by evaluating the amount of entanglement for a class of bound entangled states.

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