Characterization and properties of weakly optimal entanglement witnesses
Abstract
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 $W^{wopt}=\sigmac_{\sigma}^{max} I$, where $c_{\sigma}^{max}$ is a nonnegative 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 give an application of weakly optimal witnesses for constructing entanglement witnesses in a larger Hilbert space by extending the result of [P. Badzicag {\it et al}, Phys. Rev. A {\bf 88}, 010301(R) (2013)], and we examine their geometric properties.
 Publication:

arXiv eprints
 Pub Date:
 July 2014
 arXiv:
 arXiv:1407.0870
 Bibcode:
 2014arXiv1407.0870W
 Keywords:

 Quantum Physics
 EPrint:
 13 pages, 2 figures, has been extensively redrafted and restructured