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Bell's theorem proves that quantum theory is inconsistent with local physical models. It has propelled research in the foundations of quantum theory and quantum information science. As a fundamental feature of quantum theory, it impacts…

Bell's Theorem requires any theory which obeys the technical definitions of Free Choice and Local Causality to satisfy the Bell inequality. Invariant set theory is a finite theory of quantum physics which violates the Bell inequality…

The problem of the existence of nonlocal effects in Quantum Mechanics is discussed. The problem is divided in two: the first ('soft') one is to explain the violation of Bell's inequalities as a statistical magnitude. This can be achieved by…

The strength of classical correlations is subject to certain constraints, commonly known as Bell inequalities. Violation of these inequalities is the manifestation of nonlocality---displayed, in particular, by quantum mechanics, meaning…

It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in…

Quantum non-locality has become a popular term. Yet, its precise meaning, and even its mere existence, is the subject of controversies. The main cause of the controversies is the never ending discussion on the appropriate definitions of…

The use of the so-called entropic inequalities is revisited in the light of new quantum correlation measures, specially nonlocality. We introduce the concept of {\it classicality} as the non-violation of these classical inequalities by…

The 1964 theorem of John Bell shows that no model that reproduces the predictions of quantum mechanics can simultaneously satisfy the assumptions of locality and determinism. On the other hand, the assumptions of \emph{signal locality} plus…

By assuming a deterministic evolution of quantum systems and taking realism into account, we carefully build a hidden variable theory for Quantum Mechanics based on the notion of ontological states proposed by 't Hooft. We view these…

Between 1964 and 1990, the notion of nonlocality in Bell's papers underwent a profound change as his nonlocality theorem gradually became detached from quantum mechanics, and referred to wider probabilistic theories involving correlations…

Complementarity and nonlocality are two characteristic traits of quantum physics that distinguishes it from classical physics. In this paper, we prove that the complementarity between global and local observables in Bell's experiment sets…

Nonlocality and contextuality are at the root of conceptual puzzles in quantum mechanics, and are key resources for quantum advantage in information-processing tasks. Bell nonlocality is best understood as the incompatibility between…

According to a widespread view, the Bell theorem establishes the untenability of so-called 'local realism'. On the basis of this view, recent proposals by Leggett, Zeilinger and others have been developed according to which it can be proved…

Bell's theorem is a statement by which averages obtained from specific types of statistical distributions must conform to a family of inequalities. These models, in accordance with the EPR argument, provide for the simultaneous existence of…

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…

For a system composed of two particles Bell's theorem asserts that averages of physical quantities determined from local variables must conform to a family of inequalities. In this work we show that a classical model containing a local…

The logical foundations of Bell's inequality are reexamined. We argue that the form of the reality condition that underpins Bell's inequality comes from the requirement of solving the quantum measurement problem. Hence any violation of…

A connection is revealed between the superposition principle and locality. A self consistent interpretation of the superposition principle is put forth, from which it is shown that quantum mechanics may be a local statistical theory. Then…

In a old paper by G. Lochak, it is claimed that the Bell definition of a hidden variable is in conflict with the formalism of quantum mechanics. This result implies that it is not necessary to invoke non locality to explain the violation of…

Recent experiments allowed concluding that Bell-type inequalities are indeed violated thus it is important to understand what it means and how can we explain the existence of strong correlations between outcomes of distant measurements. Do…