Generalized concentratable entanglement via parallelized permutation tests

Physical Review Research, vol. 7

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.

Authors 3

1. Johannes Knörzer

   ETH Zurich · ETH Institute for Theoretical Studies

   Affiliation as printed

   ETH Zurich

   Institute for Theoretical Studies, ETH Zurich, 8092 Zurich, Switzerland

2. Zherui Jerry Wang Aachen Instituut-Lorentz

   Leiden University · Okinawa Institute of Science and Technology Graduate University

   Affiliation as printed

   Okinawa Institute of Science and Technology Graduate University

   Universiteit Leiden

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands

   Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan

3. Jordi Tura Aachen

   Leiden University

   Affiliation as printed

   Universiteit Leiden