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

Ray Ganardi; Piotr Masajada; Moein Naseri; Alexander Streltsov

doi:10.22331/q-2025-03-20-1666

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

Ray Ganardi^1,2, Piotr Masajada³, Moein Naseri¹, and Alexander Streltsov³

¹Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
²School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371
³Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5B, 02-106 Warsaw, Poland

Published:	2025-03-20, volume 9, page 1666
Editor:	Paul Skrzypczyk
Eprint:	arXiv:2311.11820v3
Doi:	https://doi.org/10.22331/q-2025-03-20-1666
Citation:	Quantum 9, 1666 (2025).

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Abstract

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 investigate 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 $\textit{purity-entanglement complementarity}$. 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.

► BibTeX data

@article{Ganardi2025localpurity,
  doi = {10.22331/q-2025-03-20-1666},
  url = {https://doi.org/10.22331/q-2025-03-20-1666},
  title = {Local {P}urity {D}istillation in {Q}uantum {S}ystems: {E}xploring the {C}omplementarity {B}etween {P}urity and {E}ntanglement},
  author = {Ganardi, Ray and Masajada, Piotr and Naseri, Moein and Streltsov, Alexander},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1666},
  month = mar,
  year = {2025}
}

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Cited by

[1] Piotr Masajada, Marco Fellous-Asiani, and Alexander Streltsov, "Optimizing entanglement distribution via noisy quantum channels", Physical Review A 113 5, 052414 (2026).

[2] Karol Horodecki, Marek Winczewski, Leonard Sikorski, Paweł Mazurek, Mikołaj Czechlewski, and Raja Yehia, "Quantification of the energy consumption of entanglement distribution", arXiv:2507.23108, (2025).

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