Characterization and properties of weakly optimal entanglement witnesses

@article{Wang2014CharacterizationAP,
  title={Characterization and properties of weakly optimal entanglement witnesses},
  author={Banghai Wang and Hai-Ru Xu and Steve Campbell and Simone Severini},
  journal={Quantum Inf. Comput.},
  year={2014},
  volume={15},
  pages={1109-1121}
}
We present an analysis of the properties and characteristics of weakly optimal entanglement witnesses, that is witnesses whose expectation value vanishes on at least one product vector. Any weakly optimal entanglement witness can be written as the form of $W^{wopt}=\sigma-c_{\sigma}^{max} I$, where $c_{\sigma}^{max}$ is a non-negative number and $I$ is the identity matrix. We show the relation between the weakly optimal witness $W^{wopt}$ and the eigenvalues of the separable states $\sigma… 

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