Characterization of separable states and entanglement witnesses

By Maciej Lewenstein, B. Kraus, Pawel Horodecki, J. I. Cirac. 2000

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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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/3ef88c5cf6ae8875f8faf7de7c8f7b162df52534