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Characterization and properties of weakly optimal entanglement witnesses

Wang, B-H; Xu, H-R; Campbell, S; Severini, S; (2015) Characterization and properties of weakly optimal entanglement witnesses. Quantum Information and Computation , 15 (13-14) pp. 1109-1121. Green open access

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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 Wwopt = σ − c max σ I, where c max σ is a non-negative number and I is the identity matrix. We show the relation between the weakly optimal witness Wwopt and the eigenvalues of the separable states σ. Further we give an application of weakly optimal witnesses for constructing entanglement witnesses in a larger Hilbert space by extending the result of [P. Badzia¸g et al, Phys. Rev. A 88, 010301(R) (2013)], and we examine their geometric properties.

Type: Article
Title: Characterization and properties of weakly optimal entanglement witnesses
Open access status: An open access version is available from UCL Discovery
Publisher version: http://www.rintonpress.com/journals/qiconline.html
Language: English
Additional information: This is the published version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Weakly optimal witnesses, Properties and Criteria, Minimum or maximum eigenvalue, Geometric properties
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/1511935
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