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arXiv · 1204.6596

Optimality for indecomposable entanglement witnesses

Kil-Chan Ha·Seung-Hyeok Kye
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Abstract

We examine various notions related with the optimality for entanglement witnesses arising from Choi type positive linear maps. We found examples of optimal entanglement witnesses which are non-decomposable, but which are not `non-decomposable optimal entanglement witnesses' in the sense of [M. Lewenstein, B. Kraus, J. Cirac, and P. Horodecki, Phys. Rev. A 62, 052310 (2000)]. We suggest to use the term `PPTES witness' and `optimal PPTES witness' in the places of `non-decomposable entanglement witness' and `non-decomposable optimal entanglement witnesses' in order to avoid possible confusion. We also found examples of non-extremal optimal entanglement witnesses which are indecomposable.

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Kil-Chan Ha, Seung-Hyeok Kye. 2012-04-30. Optimality for indecomposable entanglement witnesses. https://doi.org/10.1103/physreva.86.034301

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