Quantum separability criteria based on realignment moments

TL;DR

This paper introduces new quantum entanglement detection criteria based on realignment moments, extending previous methods that used partial transposed moments, and demonstrates their effectiveness through detailed examples.

Contribution

It proposes novel entanglement criteria utilizing realignment moments, providing an alternative approach to existing PT-moment based methods.

Findings

Realignment moments can identify quantum entanglement effectively.

The criteria extend the toolkit for entanglement detection beyond PT-moment methods.

Examples demonstrate the practical applicability of the proposed criteria.

Abstract

Quantum entanglement is the core resource in quantum information processing and quantum computing. It is an significant challenge to effectively characterize the entanglement of quantum states. Recently, elegant separability criterion is presented in [Phys. Rev. Lett. 125, 200501 (2020)] by Elben et al. based on the first three partially transposed (PT) moments of density matrices. Then in [Phys. Rev. Lett. 127, 060504 (2021)] Yu \emph{et al.} proposed two general powerful criteria based on the PT moments. In this paper, based on the realignment operations of matrices we propose entanglement detection criteria in terms of such realignment moments. We show by detailed example that the realignment moments can also be used to identify quantum entanglement.