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We give a set of necessary conditions for locality in bipartite systems, which include and generalize known Bell's inequalities. Each condition corresponds to a specific order of the expansion of random variables defined on graphs, in terms…

Bell's theorem cannot be proved if complementary measurements have to be represented by random variables which cannot be added or multiplied. One such case occurs if their domains are not identical. The case more directly related to the…

Many solid-state quantum platforms do not permit sharp, projective measurements but instead yield continuous voltage or field traces under weak, non-demolition readout. In such systems, standard Bell tests based on dichotomic projective…

The violation of Bell inequalities seems to establish an important fact about the world: that it is non-local. However, this result relies on the assumption of the statistical independence of the measurement settings with respect to…

Theoretical considerations of Bell-inequality experiments usually assume identically prepared and independent pairs of particles. Here we consider pairs that exhibit both intra- and inter-pair entanglement. The pairs are taken from a large…

The Bell theorem is explored in terms of a trade-off relation between underlying assumptions within the hidden variable model framework. In this paper, recognizing the incorporation of hidden variables as one of the fundamental assumptions,…

In the first part of this presentation (sections 2 to 6), I show that Bell's Inequalities provide a quantitative criterion to test "reasonable" Supplementary Parameters Theories versus Quantum Mechanics. Following Bell, I first explain the…

It has been shown that there is a small possibility to experimentally violate the CHSH Bell inequality in a 'classical' context. The probability of such a violation has been estimated in the framework of a classical probabilistic model in…

Derivation of the full set of Bell inequalities involving correlation functions, for two parties, with binary observables, and N possible local settings is not as easy as it seemed. The proof of v1 is wrong. Additionaly one can find a…

The aim of this note is to attract attention of experimenters to the original Bell (OB) inequality which was shadowed by the common consideration of the CHSH inequality. There are two reasons to test the OB inequality and not the CHSH…

Bell theorems show how to experimentally falsify local realism. Conclusive falsification is highly desirable as it would provide support for the most profoundly counterintuitive feature of quantum theory - nonlocality. Despite the…

In Phys. Rev. A 101, 022117 (2020), it was argued that Bell inequalities are based on classical, not quantum, physics, and hence their violation in experiments provides no support for the claimed existence of peculiar nonlocal and…

Bell's theorem of 1965 is a proof that all realistic interpretations of quantum mechanics must be non-local. Bell's theorem consists of two parts: first a correlation inequality is derived that must be satisfied by all local realistic…

We show that paradoxical consequences of violations of Bell's inequality are induced by the use of an unsuitable probabilistic description for the EPR-Bohm-Bell experiment. The conventional description (due to Bell) is based on a…

Bell's theorem supposedly demonstrates an irreconcilable conflict between quantum mechanics and local, realistic hidden variable theories. In this paper we show that all experiments that aim to prove Bell's theorem do not actually achieve…

It is well known that jointly measurable observables cannot lead to a violation of any Bell inequality - independent of the state and the measurements chosen at the other site. In this letter we prove the converse: every pair of…

Bell's Theorem witnesses that the predictions of quantum theory cannot be reproduced by theories of local hidden variables in which observers can choose their measurements independently of the source. Working out an idea of Branciard,…

There are increasingly suggestions for computer simulations of quantum statistics which try to violate Bell type inequalities via classical, common cause correlations. The Clauser-Horne-Shimony-Holt (CHSH) inequality is very robust.…

Bell inequalities are one of the cornerstones of quantum foundations, and fundamental tools for quantum technologies. Recently, the scientific community worldwide has put a lot of effort towards them, which culminated with loophole-free…

Bell's inequalities can be understood in three different ways depending on whether the numbers featuring in the inequalities are interpreted as classical probabilities, classical conditional probabilities, or quantum probabilities. In the…