A Geometric picture of entanglement and Bell inequalities

Nov, 2001
19 pages
Published in:
  • Phys.Rev.A 66 (2002) 032319
e-Print:
Report number:
  • UWTHPH-2001-47

Citations per year

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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