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arXiv · 1301.7558

Optimality of a class of entanglement witnesses for $3\otimes 3$ systems

Xiaofei Qi·Jinchuan Hou
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Abstract

Let $\Phi_{t,\pi}: M_3({\mathbb C}) \rightarrow M_3({\mathbb C})$ be a linear map defined by $\Phi_{t,\pi}(A)=(3-t)\sum_{i=1}^3E_{ii}AE_{ii}+t\sum_{i=1}^3E_{i,\pi(i)}AE_{i,\pi(i)}^\dag-A$, where $0\leq t\leq 3$ and $\pi$ is a permutation of $(1,2,3)$. We show that the Hermitian matrix $W_{\Phi_{t,\pi}}$ induced by $\Phi_{t,\pi}$ is an optimal entanglement witness if and only if $t=1$ and $\pi$ is cyclic.

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Xiaofei Qi, Jinchuan Hou. 2013-01-31. Optimality of a class of entanglement witnesses for $3\otimes 3$ systems. https://doi.org/10.1007/s10773-013-1649-5

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