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Entanglement and its consequences - in particular the violation of Bell inequalities, which defies our concepts of realism and locality - have been proven to play key roles in Nature by many experiments for various quantum systems.…

Objections to the use of inequalities to address foundational issues are considered and shown to be invalid. The Clauser-Horne (CH) inequality is considered and interpreted in this light. It is shown that, applied correctly, the CH…

In a recent article, Kiukas and Werner claim to have shown that Bohmian Mechanics does not make the same empirical predictions as ordinary Quantum Mechanics. More precisely, they have shown that ordinary Quantum Mechanics predicts maximal…

A recent experiment yielding results in agreement with quantum theory and violating Bell inequalities was interpreted [Nature 526 (29 Octobert 2015) p. 682 and p. 649] as ruling out any local realistic theory of nature. But quantum theory…

A locally causal hidden-variable theory of quantum physics need not be constrained by the Bell inequalities if this theory also partially violates the measurement independence condition. However, such violation can appear unphysical,…

The theorem developed by John Bell constituted the starting point of a revolution that translated a philosophical question about the nature of reality into the broad and intense field of research of the quantum information technologies. We…

The Clauser-Horne-Shimony-Holt (CHSH) inequality is a constraint that local theories must obey. Quantum Mechanics predicts a violation of this inequality in certain experimental settings. Treatments of this subject frequently make…

For the Bell scenario with two parties and two binary observables per party, it is known that the no-signaling polytope is the polyhedral dual (polar) of the Bell polytope. Computational evidence suggests that this duality also holds for…

We explore quantum nonlocality in one of the simplest bipartite scenarios. Several new facet-defining Bell inequalities for the {[3 3 3] [3 3 3]} scenario are obtained with their quantum violations analyzed in details. Surprisingly, all…

Bell inequalities are derived for any number of observers, any number of alternative setups for each one of them, and any number of distinct outcomes for each experiment. It is shown that if a physical system consists of several distant…

Relations connecting violation of any Bell inequalities and the complementarity between visibility and distinguishability in the interferometric experiments with different sources of decoherence are presented. A boundary of local-realistic…

A correlation inequality is derived from local realism and a supplementary assumption. Unlike Clauser-Horne (CH) inequality [or Clauser-Horne-Shimony-Holt (CHSH) inequality] which is violated by quantum mechanics by a factor of $\sqrt 2$,…

The assumption of local realism in a Bell locality scenario imposes non-trivial conditions on the Shannon entropies of the associated probability distributions, expressed by linear entropic Bell inequalities. In principle, these entropic…

The empirical proof of Bell inequality violations was a landmark moment for research into quantum foundations. It commits us to a universe without strict relativistic locality or requires that we escape through a potential loophole like…

Bell's theorem revealed that a local hidden-variable model cannot completely reproduce the quantum mechanical predictions. Bell's inequality provides an upper bound under the locality and reality assumptions that can be violated by…

A method for construction of the multipartite Clauser-Horne-Shimony-Holt (CHSH) type Bell inequalities, for the case of local binary observables, is presented. The standard CHSH-type Bell inequalities can be obtained as special cases. A…

Violation of Bell inequalities is an essential requirement for many quantum information and communication protocols. In high-dimensional systems, Bell inequality tests face the challenge of implementing genuinely multi-outcome measurements,…

The Bell theorem stands as an insuperable roadblock in the path to a very desired intuitive solution of the EPR paradox and, hence, it lies at the core of the current lack of a clear interpretation of the quantum formalism. The theorem…

Local realism is the worldview in which physical properties of objects exist independently of measurement and where physical influences cannot travel faster than the speed of light. Bell's theorem states that this worldview is incompatible…

We point out a loophole in the derivation of the Bell inequalities in the form proposed by Clauser, Horne, Shimony and Holt (CHSH). In this derivation it is assumed that statistical independence is a necessary consequence of locality, but…