Geometric picture of entanglement and Bell inequalities

R. A. Bertlmann, H. Narnhofer, and W. Thirring
Phys. Rev. A 66, 032319 – Published 27 September 2002
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Abstract

We work in the real Hilbert space Hs of Hermitian Hilbert-Schmidt operators and show that the entanglement witness which shows the maximal violation of a generalized Bell inequality (GBI) is a tangent functional to the convex set SHs of separable states. This violation equals the Euclidean distance in Hs of the entangled state to S and thus entanglement, GBI, and tangent functional are only different aspects of the same geometric picture. This is explicitly illustrated in the example of two spins, where also a comparison with familiar Bell inequalities is presented.

  • Received 22 November 2001

DOI:https://doi.org/10.1103/PhysRevA.66.032319

©2002 American Physical Society

Authors & Affiliations

R. A. Bertlmann, H. Narnhofer, and W. Thirring

  • Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, A-1090 Wien, Austria

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Vol. 66, Iss. 3 — September 2002

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