Separability in terms of a single entanglement witness

Details Separability in terms of a single entanglement witness Separability in terms of a single entanglement witness

2007-03-12

arxiv.org/abs/quant-ph/0703097v1

Physics

Quantum Physics

4 pages, 1 figure, RevTex

Scientific paper

Separability problem is formulated in terms of a characterization of a {\it single} entanglement witness operator. More specifically, we show that any (in general multipartite) state $\varrho$ is separable if and only if a specially constructed entanglement witness $W_{\varrho}$ (which may always be chosen decomposable) is weakly optimal, i.e., its expectation value vanishes on at least one product vector. This changes the conceptual aspect of the separability problem and rises some new questions about properties of positive maps.

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