A general scheme for construction of scalar separability criteria from positive maps

Details A general scheme for construction of scalar separability criteria from positive maps A general scheme for construction of scalar separability criteria from positive maps

2007-09-24

arxiv.org/abs/0709.3779v2

Physical Review A 77, 010303(R) (2008)

Physics

Quantum Physics

RevTex, 5 pages, 2 figures, the revised version

Scientific paper

10.1103/PhysRevA.77.010303

We present a general scheme that allows for construction of scalar separability criteria from positive but not completely positive maps. The concept is based on a decomposition of every positive map $\Lambda$ into a difference of two completely positive maps $\Lambda_1$, $\Lambda_2$, i.e., $\Lambda=\Lambda_1-\Lambda_2$. The scheme may be also treated as a generalization of the known entropic inequalities, which are obtained from the reduction map. An analysis performed on few classes of states shows that the new scalar criteria are stronger than the entropic inequalities and furthermore, when derived from indecomposable maps allow for detection of bound entanglement.

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