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arXiv · 1108.0456

Necessary conditions for optimality of decomposable entanglement witnesses

Seung-Hyeok Kye
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Abstract

It is well known that the support of an optimal decomposable entanglement witness is completely entangled. We add two more necessary conditions for the optimality: The orthogonal complement of the support must have a nonzero product vector; another one will be given in terms of related faces of a convex cone. With these necessary conditions, we show that there exist examples of non-optimal decomposable entanglement witnesses which are the partial transposes of positive semi-definite matrices supported on completely entangled spaces, whenever both of the local dimensions are greater than or equal to three.

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Seung-Hyeok Kye. 2011-08-02. Necessary conditions for optimality of decomposable entanglement witnesses. https://doi.org/10.1016/s0034-4877(13)60007-5

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