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It is explained on a physical basis how contextuality allows Bell inequalities to be violated, without bringing an implication on locality or realism. The point is that the initial values of the hidden variables of the detectors are…

In a local realist world view, physical properties are defined prior to and independent of measurement, and no physical influence can propagate faster than the speed of light. Proper experimental violation of a Bell inequality would show…

A violation of Bell local realism inequalities in Clauser-Horn-Shimony-Holt (CHSH) form has been discovered in a relativistic GedanknExperiment. This means that there are no definite joint probabilities and this finds a classical…

Bell inequalities or Bell-like experiments are supposed to test hidden variable theories based on three intuitive assumptions: determinism, locality and measurement independence. If one of the assumptions of Bell inequality is properly…

Despite claims that Bell's inequalities are based on the Einstein locality condition, or equivalent, all derivations make an identical mathematical assumption: that local hidden-variable theories produce a set of positive-definite…

In this paper, we highlight how any Bell inequality for a configuration involving $n$ parties each performing one of $m$ binary-outcome measurements has a canonical form that is no-signalling-projection invariant. Specifically, the…

Based on the new general framework for the probabilistic description of experiments, introduced in quant-ph/0305126, quant-ph/0312199, we analyze in mathematical terms the link between the validity of Bell-type inequalities under joint…

In this Comment we show that Cabello's proof of Bell's theorem without inequalities [Phys. Rev. Lett. 91, 230403 (2003)] does not exhibit two of the three "remarkable properties" which the proof is claimed to possess. More precisely it is…

Bell nonlocality and Kochen-Specker contextuality are two remarkable nonclassical features of quantum theory, related to strong correlations between outcomes of measurements performed on quantum systems. Both phenomena can be witnessed by…

It is shown that the data of the Hensen et al. Bell test experiment exhibits anomalous postselection that can fully account for the apparent violation of the CHSH inequality. A simulation of a local realist model implementing similar…

We computationally investigate the complete polytope of Bell inequalities for 2 particles with small numbers of possible measurements and outcomes. Our approach is limited by Pitowsky's connection of this problem to the computationally hard…

Counterfactual definiteness is supposed to underlie the Bell theorem. An old controversy exists among those who reject the theorem implications by rejecting counterfactual definiteness and those who claim that, since it is a direct…

A Bell inequality is a constraint on a set of correlations whose violation can be used to certify non-locality. They are instrumental for device-independent tasks such as key distribution or randomness expansion. In this work we consider…

Bell inequalities reveal the fundamentally nonlocal character of quantum mechanics. In this regard, one of the interesting problems is to explore all possible Bell inequalities that demonstrate a gap between local and nonlocal quantum…

Some new temporal Bell inequalities are deduced under joint realism assumption, using some perfect correlation property. No locality condition is needed. When the measured system is a macroscopic system, joint realism assumption substitutes…

It is well-known that the set of statistics that can be observed in a Bell-type experiment is limited by quantum theory. Unfortunately, tools are missing to identify the precise boundary of this set. Here, we propose to study the set of…

Loophole-free violations of Bell inequalities imply that at least one of the assumptions behind local hidden-variable theories must fail. Here, we show that, if only one fails, then it has to fail completely, therefore excluding models that…

The fabled violation of Bell's inequality by the probabilistic specifications of quantum mechanics is shown to derive from a mathematical error. The inequality, designed to assess consequences of Einstein's principle of local realism,…

We analyse the proof of Bell's inequality and demonstrate that this inequality is related to one particular model of probability theory, namely Kolmogorov measure-theoretical axiomatics, 1933. We found a (numerical) statistical correction…

Contrary to what Lambare [arXiv:2008.00369] assumes, in non-Newtonian calculus (a calculus based on non-Diophantine arithmetic) an integral is typically given by a nonlinear map. This is the technical reason why all the standard proofs of…