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In contrast to the wide-spread opinion that any separable quantum statesatisfies every classical probabilistic constraint, we present a simple examplewhere a separable quantum state does not satisfy the original Bell inequalityalthough the latter inequality, in its perfect correlation form, is valid forall joint classical measurements. In a very general setting, we discussinequalities for joint experiments upon a bipartite quantum system in aseparable state. We derive quantum analogues of the original Bell inequalityand specify the conditions sufficient for a separable state to satisfy theoriginal Bell inequality. We introduce the extended CHSH inequality and provethat, for any separable quantum state, this inequality holds for a variety oflinear combinations.Comment: 13 pages, extended versio

Separability of quantum states and the violation of Bell-type inequalities