Bell Inequalities and the Separability Criterion

Details Bell Inequalities and the Separability Criterion Bell Inequalities and the Separability Criterion

1999-11-12

arxiv.org/abs/quant-ph/9911057v4

Physics Letters A Vol. 271, 319 (2000)

Physics

Quantum Physics

16 pages Revtex, typo in equation (14) corrected

Scientific paper

10.1016/S0375-9601(00)00401-1

We analyze and compare the mathematical formulations of the criterion for separability for bipartite density matrices and the Bell inequalities. We show that a violation of a Bell inequality can formally be expressed as a witness for entanglement. We also show how the criterion for separability and a description of the state by a local hidden variable theory, become equivalent when we restrict the set of local hidden variable theories to the domain of quantum mechanics. This analysis sheds light on the essential difference between the two criteria and may help us in understanding whether there exist entangled states for which the statistics of the outcomes of all possible local measurements can be described by a local hidden variable theory.

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