A Geometric Picture of Entanglement and Bell Inequalities

Details A Geometric Picture of Entanglement and Bell Inequalities A Geometric Picture of Entanglement and Bell Inequalities

2001-11-21

arxiv.org/abs/quant-ph/0111116v3

Phys.Rev. A66 (2002) 032319

Physics

Quantum Physics

17 pages, 5 figures, 4 references added

Scientific paper

10.1103/PhysRevA.66.032319

We work in the real Hilbert space H_s of hermitian Hilbert-Schmid 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 S subset H_s of separable states. This violation equals the euclidean distance in H_s 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.

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