A complete proof of Korbicz et al [\emph{Phys. Rev. A}{\bf 78} 062105 (2008)] conjecture

Details A complete proof of Korbicz et al [\emph{Phys. Rev. A}{\bf 78} 062105 (2008)] conjecture A complete proof of Korbicz et al [\emph{Phys. Rev. A}{\bf 78} 062105 (2008)] conjecture

2011-06-26

arxiv.org/abs/1106.5233v1

Physics

Quantum Physics

4pages

Scientific paper

We show a general method to construct finer and optimal entanglement witnesses. Based on this result, we show that there exist infinite entanglement witnesses or only an optimal entanglement witness for a given entangled state. Furthermore, We show that any entanglement witness $W$ can be constructed from a separable density matrix $\sigma$ in the form as $W=\sigma-c_{\sigma} I$, where $\sigma$ is a separable density matrix, $c_{\sigma}$ is a non-negative number and $I$ is the identity matrix. Based on this result, we given a complete proof of Korbicz et al [\emph{Phys. Rev. A}{\bf 78} 062105 (2008)] conjecture.

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