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

Abstract

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.

arXiv comment13 pages, extended version

References in corpus (2)

• "Local Realism", Bell's Theorem and Quantum "Locally Realistic" Inequalities
• General Probabilistic Framework of Randomness

Cited by in corpus (6)

• Bipartite Bell inequalities for hyperentangled states
• Evaluating the Maximal Violation of the Original Bell Inequality by Two-Qudit States Exhibiting Perfect Correlations/Anticorrelations
• Class of bipartite quantum states satisfying the original Bell inequality
• Threshold bounds for noisy bipartite states
• Comment on "Separability of quantum states and the violation of Bell-type inequalities"
• Local hidden variable modelling, classicality, quantum separability, and the original Bell inequality