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arXiv:0805.1632 · Journal of Physics A Mathematical and Theoretical

Separability and entanglement of quantum states based on covariance matrices

Ming Li, Shao-Ming Fei, Zhi-Xi Wang

Published Apr 30, 2008• 17 citations
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Abstract

We investigate the separability of quantum states based on covariance matrices. Separability criteria are presented for multipartite states. The lower bound of concurrence proposed in Vicente (2007 Phys. Rev. A 75 052320) is improved by optimizing the local orthonormal observables.
DOI
10.1088/1751-8113/41/20/202002

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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, tighter 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.