Liu, Xiaoyu

Generalized Concentratable Entanglement via Parallelized Permutation Tests

Xiaoyu Liu  - Leiden University, Netherlands

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. However, higher powers of CE estimated across multiple state copies has not been investigated. In this talk, I will introduce a new class of multipartite entanglement measures, Generalized Concentratable Entanglement (GCE), that can be efficiently estimated on a quantum processor using parallelized permutation tests across a prime number of state copies. We highlight its natural correspondence to quantum Tsallis entropies and conjecture a new entropic inequality that may be of independent interest. 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).