Generalized Concentratable Entanglement via Parallelized Permutation Tests

TL;DR

This paper introduces Generalized Concentratable Entanglement (GCE), a new multipartite entanglement measure that can be efficiently estimated on quantum computers using parallelized permutation tests, improving entanglement quantification.

Contribution

It defines GCE measures, connects them to quantum Tsallis entropies, and demonstrates efficient measurement methods and improved error bounds for multipartite entanglement estimation.

Findings

GCE can be efficiently measured using parallelized permutation tests.

Increased state copies improve error bounds in entanglement estimation.

GCE remains a valid entanglement monotone under LOCC operations.

Abstract

Multipartite entanglement is an essential resource for quantum information theory and technologies, but its quantification has been a persistent challenge. Recently, Concentratable Entanglement (CE) has been introduced as a promising candidate for a multipartite entanglement measure, which can be efficiently estimated across two state copies. In this work, we introduce Generalized Concentratable Entanglement (GCE) measures, highlight a natural correspondence to quantum Tsallis entropies, and conjecture a new entropic inequality that may be of independent interest. We show how to efficiently measure the GCE in a quantum computer, using parallelized permutation tests across a prime number of state copies. We exemplify the practicality of such computation for probabilistic entanglement concentration into W states with three state copies. Moreover, we show that an increased number of state copies provides an improved error bound on this family of multipartite entanglement measures in the presence of imperfections. Finally, we prove that GCE is still a well-defined entanglement monotone as its value, on average, does not increase under local operations and classical communication (LOCC).