Quantifying entanglement with covariance matrices

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.

12 pages, 1 figure

References in corpus (10)

• Entanglement detection
• Quantum information with Gaussian states
• Concurrence of arbitrary dimensional bipartite quantum states
• Estimating entanglement measures in experiments
• Covariance matrices and the separability problem
• Lower bounds on concurrence and separability conditions
• Optimal entanglement witnesses based on local orthogonal observables
• Unifying several separability conditions using the covariance matrix criterion
• Entanglement detection beyond the cross-norm or realignment criterion
• Further results on entanglement detection and quantification from the correlation matrix criterion

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• Detecting and estimating continuous-variable entanglement by local orthogonal observables
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