Relations between entanglement witnesses and Bell inequalities

Journal Article · Fri Jul 15 00:00:00 EDT 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.72.012321· OSTI ID:20718329

Hyllus, Philipp ^[1]; Guehne, Otfried ^[2]; Bruss, Dagmar ^[1]; Lewenstein, Maciej ^[1]

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1. Institut fuer Theoretische Physik, Universitaet Hannover, D-30167 Hannover (Germany)
2. Institut fuer Quantenoptik und Quanteninformation, Oesterreichische Akademie der Wissenschaften, A-6020 Innsbruck (Austria)

Bell inequalities, considered within quantum mechanics, can be regarded as nonoptimal witness operators. We discuss the relationship between such Bell witnesses and general entanglement witnesses in detail for the Bell inequality derived by Clauser, Horne, Shimony, and Holt (CHSH) [Phys. Rev. Lett. 23, 880 (1969)]. We derive bounds on how much an optimal witness has to be shifted by adding the identity operator to make it positive on all states admitting a local hidden variable model. In the opposite direction, we obtain tight bounds for the maximal proportion of the identity operator that can be subtracted from such a CHSH witness, while preserving the witness properties. Finally, we investigate the structure of CHSH witnesses directly by relating their diagonalized form to optimal witnesses of two different classes.

• OSTI ID: 20718329
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 72; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
BELL THEOREM
CORRELATIONS
ENERGY LEVELS
HIDDEN VARIABLES
QUANTUM ENTANGLEMENT
QUANTUM MECHANICS