Geometric measure of entanglement and applications to bipartite and multipartite quantum states

Journal Article · Wed Oct 01 04:00:00 EDT 2003 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.68.042307· OSTI ID:20640294

Wei, T -C; Goldbart, Paul M ^[1]

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1. Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080 (United States)

The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings [A. Shimony, Ann. NY. Acad. Sci. 755, 675 (1995); H. Barnum and N. Linden, J. Phys. A: Math. Gen. 34, 6787 (2001)], is explored for bipartite and multipartite pure and mixed states. The measure is determined analytically for arbitrary two-qubit mixed states and for generalized Werner and isotropic states, and is also applied to certain multipartite mixed states. In particular, a detailed analysis is given for arbitrary mixtures of three-qubit Greenberger-Horne-Zeilinger, W, and inverted-W states. Along the way, we point out connections of the geometric measure of entanglement with entanglement witnesses and with the Hartree approximation method.

• OSTI ID: 20640294
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 4 Vol. 68; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
CORRELATIONS
DISTANCE
EIGENFUNCTIONS
EIGENVALUES
ENERGY LEVELS
HARTREE-FOCK METHOD
MIXED STATE
MIXTURES
QUANTUM MECHANICS
USES