Characterization of separable states and entanglement witnesses

Details Characterization of separable states and entanglement witnesses Characterization of separable states and entanglement witnesses

2000-05-26

arxiv.org/abs/quant-ph/0005112v1

Physics

Quantum Physics

4 pages, 1 figure

Scientific paper

10.1103/PhysRevA.63.044304

We provide a canonical form of mixed states in bipartite quantum systems in terms of a convex combination of a separable state and a, so-called, edge state. We construct entanglement witnesses for all edge states. We present a canonical form of nondecomposable entanglement witnesses and the corresponding positive maps. We provide constructive methods for their optimization in a finite number of steps. We present a characterization of separable states using a special class of entanglement witnesses. Finally, we present a nontrivial necessary condition for entanglement witnesses and positive maps to be extremal.

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