Abstract
We work in the real Hilbert space 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 of separable states. This violation equals the Euclidean distance in 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