On separability of quantum states and the violation of Bell-type inequalities

Details On separability of quantum states and the violation of Bell-type inequalities On separability of quantum states and the violation of Bell-type inequalities

2003-10-19

arxiv.org/abs/quant-ph/0310116v2

Phys. Rev. A 69, 042102 (2004); also in Virtual J. Quantum Information 4 (2004), No 4

Physics

Quantum Physics

13 pages, extended version

Scientific paper

10.1103/PhysRevA.69.042102

In contrast to the wide-spread opinion that any separable quantum state satisfies every classical probabilistic constraint, we present a simple example where a separable quantum state does not satisfy the original Bell inequality although the latter inequality, in its perfect correlation form, is valid for all joint classical measurements. In a very general setting, we discuss inequalities for joint experiments upon a bipartite quantum system in a separable state. We derive quantum analogues of the original Bell inequality and specify the conditions sufficient for a separable state to satisfy the original Bell inequality. We introduce the extended CHSH inequality and prove that, for any separable quantum state, this inequality holds for a variety of linear combinations.

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