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Generalized concentratable entanglement via parallelized permutation tests

Xiaoyu Liu1,2, Johannes Knörzer3, Zherui Jerry Wang1,2,4, and Jordi Tura1,2

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Phys. Rev. Research 7, L032022 – Published 25 July, 2025

DOI: https://doi.org/10.1103/jtlj-qs3y

Abstract

Multipartite entanglement is an essential resource for quantum information theory and technologies, but its quantification has been a persistent challenge. Concentratable entanglement (CE), introduced recently, can be estimated from just two copies of a quantum state. Here, we propose generalized concentratable entanglement (GCE), a broader class of multipartite entanglement measures naturally tied to quantum Tsallis entropies, and present a parallelized protocol for estimating GCE across multiple state copies. Increasing the number of copies yields an improved error bound in the presence of imperfections. We prove that GCE is a well-defined entanglement monotone and conjecture some new entropic inequalities. Moreover, we demonstrate the concentration of entanglement into W states using three-state copies. Our results contribute to more robust and versatile characterizations of multipartite entanglement.

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Phys. Rev. Research 7, L032022– Published 25 July, 2025
  • Received 22 August 2024
  • Revised 6 February 2025
  • Accepted 13 June 2025
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