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Characterization of separable states and entanglement witnesses

M. Lewenstein·B. Kraus·P. Horodecki·J. I. Cirac
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Abstract

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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M. Lewenstein, B. Kraus, P. Horodecki, J. I. Cirac. 2000-05-26. Characterization of separable states and entanglement witnesses. https://doi.org/10.1103/physreva.63.044304

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