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arXiv:1608.01547 · Scientific Reports

Improved Separability Criteria Based on Bloch Representation of Density Matrices

Shu‐Qian Shen, Juan Yu, Ming Li, Shao-Ming Fei

Published Jun 28, 2016• 27 citations
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Abstract

The correlation matrices or tensors in the Bloch representation of density matrices are encoded with entanglement properties. In this paper, based on the Bloch representation of density matrices, we give some new separability criteria for bipartite and multipartite quantum states. Theoretical analysis and some examples show that the proposed criteria can be more efficient than the previous related criteria.

DOI
10.1038/srep28850

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The correlation matrices or tensors in the Bloch representation of density matrices are encoded with entanglement properties. In this paper, based on the Bloch representation of density matrices, we give some new separability criteria for bipartite and multipartite quantum states. Theoretical analysis and some examples show that the proposed criteria can be more efficient than the previous related criteria.
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The detection and quantification of quantum entanglement are central problems in quantum information science. Based on the realignment of density matrices and the vectorization of reduced density matrices, we construct a family of enhanced separability criteria for bipartite and multipartite quantum systems. Our criteria recover the previously proposed realignment-based criteria as special cases and detect more entanglement than the earlier ones. Moreover, we derive tighter lower bounds for the concurrence and the convex-roof extended negativity, criteria for detecting the genuine tripartite entanglement, and lower bounds on genuine-multipartite-entanglement concurrence. The advantages of our results are demonstrated with detailed examples.
The detection of entanglement in a bipartite state is a crucial issue in quantum information science. Based on realignment of density matrices and the vectorization of the reduced density matrices, we introduce a new set of separability criteria. The proposed separability criteria can detect more entanglement than the previous separability criteria. Moreover, we provide new criteria for detecting the genuine tripartite entanglement and lower bounds for the concurrence and convex-roof extended negativity. The advantages of results are demonstrated through detailed examples.
By combining a parameterized Hermitian matrix, the realignment matrix of the bipartite density matrix, 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.