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.
Highlights
Quantum entanglement is a fascinating phenomenon in quantum physics
The correlation matrices or tensors in the Bloch representation are encoded with entanglement properties[22,23], which can be exploited to study quantum entanglement
In ref. 24, by making use of correlation matrices, Vicente obtained the correlation matrix criterion for bipartite quantum states, which can be more efficient than the positive partial transpose (PPT) criterion[7,8] and the computable cross norm or realignment (CCNR) criterion[9,10] in many different situations
Summary
Based on Bloch Representation of Density Matrices received: 14 May 2016 accepted: 09 June 2016 Published: 28 June 2016. In this paper, based on the Bloch representation of density matrices, we give some new separability criteria for bipartite and multipartite quantum states. 24, by making use of correlation matrices, Vicente obtained the correlation matrix criterion for bipartite quantum states, which can be more efficient than the PPT criterion[7,8] and the computable cross norm or realignment (CCNR) criterion[9,10] in many different situations After that, this criterion was used to give the analytical lower bounds for the entanglement measures: concurrence and tangle[25,26], which are good supplement to the lower bounds based on PPT and CCNR criteria. By the matricizations of tensors, the correlation matrix criterion was generalized to detect non-full-separability of multipartite states[27]. An example shows that the new multipartite separability criterion can be better than the corresponding criteria obtained in refs 27, 28 and 30
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