Separability and lower bounds of quantum entanglement based on realignment

TL;DR

This paper introduces new criteria based on matrix realignment for detecting quantum entanglement and provides improved lower bounds for entanglement measures, enhancing the identification of genuine multipartite entanglement.

Contribution

It presents novel separability criteria using realignment and vectorization, along with tighter lower bounds for concurrence and negativity, applicable to bipartite and multipartite systems.

Findings

Criteria outperform existing methods in entanglement detection

New lower bounds improve estimation accuracy

Effective detection of genuine tripartite entanglement

Abstract

The detection and estimation of quantum entanglement are the essential issues in the theory of quantum entanglement. We construct matrices based on the realignment of density matrices and the vectorization of the reduced density matrices, from which a family of separability criteria are presented for both bipartite and multipartite systems. Moreover, new lower bounds of concurrence and convex-roof extended negativity are derived. Criteria are also given to detect the genuine tripartite entanglement. Lower bounds of the concurrence of genuine tripartite entanglement are presented. By detailed examples we show that our results are better than the corresponding ones in identifying and estimating quantum entanglement as well as genuine multipartite entanglement.