A Geometric picture of entanglement and Bell inequalities
Nov, 200119 pages
Published in:
- Phys.Rev.A 66 (2002) 032319
e-Print:
- quant-ph/0111116 [quant-ph]
Report number:
- UWTHPH-2001-47
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Abstract:
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.Note:
- 17 pages, 5 figures, 4 references added
References(32)
Figures(6)