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According to Bell's theorem a large class of hidden-variable models obeying Bell's notion of local causality conflict with the predictions of quantum mechanics. Recently, a Bell-type theorem has been proven using a weaker notion of local…

"Bell's theorem" can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the joint assumptions of Locality and Predetermination.…

The scientific method relies on facts, established through repeated measurements and agreed upon universally, independently of who observed them. In quantum mechanics, the objectivity of observations is not so clear, most dramatically…

Bell's theorem shows that local realistic theories place strong restrictions on observable correlations between different systems, giving rise to Bell's inequality which can be violated in experiments using entangled quantum states. Bell's…

We show how one can be led from considerations of quantum steering to Bell's theorem. We begin with Einstein's demonstration that, assuming local realism, quantum states must be in a many-to-one ("incomplete") relationship with the real…

We consider typical experiments that use Bell-inequalities to test local-realist theories of quantum mechanics and gain insight into how certain results can be obtained. We see that results against local-realism arise from some `quantum…

(A) Bell's theorem rests on a conjunction of three assumptions: realism, locality and ``free will''. A discussion of these assumptions will be presented. It will be also shown that, if one adds to the assumptions the principle or rotational…

Quantum theory violates Bell's inequality, but not to the maximum extent that is logically possible. We derive inequalities (generalizations of Cirel'son's inequality) that quantify the upper bound of the violation, both for the standard…

In this short survey article, I discuss Bell's theorem and some strategies that attempt to avoid the conclusion of non-locality. I focus on two that intersect with the philosophy of probability: (1) quantum probabilities and (2)…

We show that a single Bell's inequality with two dichotomic observables for each observer, which is originated from Hardy's nonlocality proof without inequalities, is violated by all entangled pure states of a given number of particles,…

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…

Bell's theorem is typically understood as the proof that quantum theory is incompatible with local-hidden-variable models. More generally, we can see the violation of a Bell inequality as witnessing the impossibility of explaining quantum…

Quantum nonlocality is often judged by violations of Bell-type inequalities for a given state. The computation of such violations is a global task, requiring evaluation of global correlations and subsequent testing against a Bell…

In the case of a pair of two-outcome measurements incompatibility is equivalent to Bell nonlocality. Indeed, any pair of incompatible two-outcome measurements can violate the Clauser-Horne-Shimony-Holt Bell inequality, which has been proven…

This article shows that the there is no paradox. Violation of Bell's inequalities should not be identified with a proof of non locality in quantum mechanics. A number of past experiments is reviewed, and it is concluded that the…

Derivations of two Bell's inequalities are given in a form appropriate to the interpretation of experimental data for explicit determination of all the correlations. They are arithmetic identities independent of statistical reasoning and…

Based on the quantum violation of bipartite Bell inequality, it has been demonstrated that the sharing of non-locality can be demonstrated for at most two sequential observers at one end and at most one-pair of observers at both ends. In…

Bell's Theorem proved that one cannot in general reproduce the results of quantum theory with a classical, deterministic local model. However, Einstein originally considered the case where one could define an 'element of reality', namely…

The theorem of Bell states that certain results of quantum mechanics violate inequalities that are valid for objective local random variables. We show that the inequalities of Bell are special cases of theorems found ten years earlier by…

We derive a Bell inequality based on a generalized quasiprobability function which is parameterized by one non-positive real value. Two types of known Bell inequalities formulated in terms of the Wigner and Q functions are included as…