Quantifying entanglement with covariance matrices

TL;DR

This paper introduces an entanglement quantification method using covariance matrices, providing easily computable lower bounds on concurrence for bipartite quantum systems, applicable to both continuous and finite dimensional systems.

Contribution

It proposes an entanglement parameter based on covariance matrix criteria that quantifies entanglement and offers lower bounds on concurrence, enhancing entanglement estimation methods.

Findings

Provides a new entanglement parameter based on covariance matrices.

Offers easily computable lower bounds on concurrence.

Applicable to weakly entangled bipartite states.

Abstract

Covariance matrices are a useful tool to investigate correlations and entanglement in quantum systems. They are widely used in continuous variable systems, but recently also for finite dimensional systems powerful entanglement criteria in terms of covariance matrices have been derived. We show how these results can be used for the quantification of entanglement in bipartite systems. To that aim we introduce an entanglement parameter that quantifies the violation of the covariance matrix criterion and can be used to give a lower bounds on the concurrence. These lower bounds are easily computable and give entanglement estimates for many weakly entangled states.