Positive finite rank elementary operators and characterizing entanglement of states

Details Positive finite rank elementary operators and characterizing entanglement of states Positive finite rank elementary operators and characterizing entanglement of states

2010-08-22

arxiv.org/abs/1008.3682v2

J. Phys. A: Math. Theor. 44 (2011) 215305

Physics

Quantum Physics

26 pages

Scientific paper

10.1088/1751-8113/44/21/215305

In this paper, a class of indecomposable positive finite rank elementary operators of order $(n,n)$ are constructed. This allows us to give a simple necessary and sufficient criterion for separability of pure states in bipartite systems of any dimension in terms of positive elementary operators of order $(2,2)$ and get some new mixed entangled states that can not be detected by the positive partial transpose (PPT) criterion and the realignment criterion.

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