Separability criteria based on the realignment of density matrices and reduced density matrices

TL;DR

This paper introduces a new family of separability criteria for quantum states that outperform existing methods like CCNR, especially in detecting multipartite entanglement through realignment and reduced density matrices.

Contribution

The authors propose a novel set of separability criteria combining realignment matrices and reduced density matrices, which are more effective than previous criteria such as CCNR.

Findings

New criteria are stronger than CCNR for bipartite states.

Criteria can detect multipartite entanglement more efficiently.

Examples demonstrate improved detection over existing methods.

Abstract

By combining a parameterized Hermitian matrix, the realignment matrix of the bipartite density matrix $\rho$ and the vectorization of its reduced density matrices, we present a family of separability criteria, which are stronger than the computable cross norm or realignment (CCNR) criterion. With linear contraction methods, the proposed criteria can be used to detect the multipartite entangled states that are biseparable under any bipartite partitions. Moreover, we show by examples that the presented multipartite separability criteria can be more efficient than the corresponding multipartite realignment criterion based on CCNR, multipartite correlation tensor criterion and multipartite covariance matrix criterion.