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Physical Review A

Sufficient criterion for separability of bipartite states

Kil-Chan Ha

Published Jul 30, 2010• 3 citations
Publisher

Abstract

We observe a convex subset of the set of all $M\ensuremath{\bigotimes}N$ separable states. On the basis of this observation, we give an alternative sufficient condition for separability of bipartite states. This criterion gives rise to a family of quantum channels which are entanglement breaking.

DOI
10.1103/physreva.82.014102

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We observe a convex subset of the set of all M\ensuremath⨂NM\ensuremath{\bigotimes}NM\ensuremath⨂N separable states. On the basis of this observation, we give an alternative sufficient condition for separability of bipartite states. This criterion gives rise to a family of quantum channels which are entanglement breaking.
A new criterion necessary and sufficient for the separability of pure bipartite systems for arbitrary finite dimensions is demonstrated; and the corresponding finer quantitative measures or characterizations of entanglement (beyond mere separability or non-separability determination) are discussed. Based on this criterion, we proved that the well-known Peres-Horodecki positivity-of-partial-transform criterion is also necessary and sufficient for separability in the case of pure bipartite systems. The maximum value of entanglement, and the corresponding maximally-entangled states are also worked out in detail.