Correlation based entanglement criteria for bipartite systems

TL;DR

This paper presents new correlation-based inequalities for detecting entanglement in bipartite quantum systems, outperforming existing criteria and incorporating purity-related terms that can be experimentally measured.

Contribution

Introduction of a novel class of entanglement criteria based on low order correlations applicable to various systems, including a measurable purity term.

Findings

Criteria outperform existing correlation-based entanglement tests

Applicable to Hermitian and non-Hermitian operators

Includes a measurable purity-related term

Abstract

We introduce a class of inequalities based on low order correlations of operators to detect entanglement in bipartite systems. The operators may either be Hermitian or non-Hermitian and are applicable to any physical system or class of states. Testing the criteria on example systems reveals that they outperform other common correlation based criteria, such as those by Duan-Giedke-Cirac-Zoller and Hillery-Zubairy. One unusual feature of the criteria is that it includes a term involving the average of the density matrix squared, related to the purity of the system. We discuss how such a term could be measured in relation to the criteria.