By Cox R.T., Hubbard J.C.
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Extra info for A Statistical Quantum Theory of Regular Reflection and Refraction
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93] we have studied the class of entanglement witnesses; considering density matrices (states) and operators (entanglement witnesses) as elements of a Hilbert space it turns out that entanglement witnesses are tangent functionals to the set of separable states. Considering the Euclidean distance of the vectors in Hilbert space for entangled and separable states we have found the following Theorem. Theorem: Bertlmann–Narnhofer–Thirring  • The Euclidean distance of an entangled state to the separable states is equal to the maximal violation of the GBI with the tangent functional as entanglement witness!
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A Statistical Quantum Theory of Regular Reflection and Refraction by Cox R.T., Hubbard J.C.