Relation between entanglement measures and Bell inequalities for three qubits

Journal Article · Mon Mar 01 04:00:00 EST 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.69.032317· OSTI ID:20640843

Emary, C; Beenakker, C W.J. ^[1]

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1. Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden (Netherlands)

For two qubits in a pure state there exists a one-to-one relation between the entanglement measure (the concurrence C) and the maximal violation M of a Bell inequality. No such relation exists for the three-qubit analog of C (the tangle {tau}), but we have found that numerical data is consistent with a simple set of upper and lower bounds for {tau} given M. The bounds on {tau} become tighter with increasing M, so they are of practical use. The Svetlichny form of the Bell inequality gives tighter bounds than the Mermin form. We show that the bounds can be tightened further if the tangle is replaced by an entanglement monotone that can identify both the W state and the Greenberger-Horne-Zeilinger state.

• OSTI ID: 20640843
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 3 Vol. 69; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
BELL THEOREM
CORRELATIONS
ENERGY LEVELS
INFORMATION THEORY
QUANTUM MECHANICS