Characterization and properties of weakly optimal entanglement witnesses
arXiv preprint arXiv:1407.0870, 2014•arxiv.org
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 $. Further we …
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 $. Further we …
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 , where is a non-negative number and is the identity matrix. We show the relation between the weakly optimal witness and the eigenvalues of the separable states . Further we give an application of weakly optimal witnesses for constructing entanglement witnesses in a larger Hilbert space by extending the result of [P. Badzi\c{a}g {\it et al}, Phys. Rev. A {\bf 88}, 010301(R) (2013)], and we examine their geometric properties.
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