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arXiv · 1304.2040

Checking the optimality of entanglement witnesses: an application to structural physical approximations

R. Augusiak·J. Bae·J. Tura·M. Lewenstein
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Abstract

In 2008, the conjecture that structural physical approximations to optimal entanglement witnesses are separable states (in general unnormalized) was posed. In an attempt to disprove it, in [K.-C. Ha and S.-H. Kye, Separable states with unique decompositions, arXiv:1210.1088v3], Ha and Kye proposed a decomposable entanglement witness whose SPA is entangled and argued that it is optimal. In this note, which is based on a comment to the latter work [R. Augusiak et al., Comment on "Separable states with unique decompositions", arXiv:1304.2040v1], we show, both analytically and numerically, that this entanglement witness is not optimal, and as such it is not a counterexample to the conjecture. To this end, we make use of a method for checking optimality of entanglement witnesses developed already in [M. Lewenstein et al., Phys. Rev. A 62, 052310 (2000)], however, hardly exploited so far in the literature.

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R. Augusiak, J. Bae, J. Tura, M. Lewenstein. 2013-04-07. Checking the optimality of entanglement witnesses: an application to structural physical approximations. https://doi.org/10.1088/1751-8113/47/6/065301

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