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Mathematics equivalent to Bell's derivation of the inequalities, also allows a local hidden variables explanation for the correlation between distant measurements.
The Bell-Clauser-Horne-Shimony-Holt (BCHSH) inequality, which is proven in the context of the local hidden variable theory, has been used as a test to reveal failure of the hidden variable theory and to prove validity of the quantum theory.…
We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities…
Bell inequalities characterize the boundary of the local-realist correlation polytope -- the set of joint probability distributions achievable by classical hidden-variable models. Quantum mechanics exceeds this boundary through…
Nonlocality, evidenced by the violation of Bell inequalities, not only signifies entanglement but also highlights measurement incompatibility in quantum systems. Utilizing the generalized Clauser-Horne-Shimony-Holt (CHSH) Bell inequality,…
For linear combinations of quantum product averages in an arbitrary bipartite state, we derive new quantum Bell-form and CHSH-form inequalities with the right-hand sides expressed in terms of a bipartite state. This allows us to specify in…
We present the results of two tests where a sample of human participants were asked to make judgements about the conceptual combinations {\it The Animal Acts} and {\it The Animal eats the Food}. Both tests significantly violate the…
To reproduce in a local hidden variables theory correlations that violate Bell inequalities, communication must occur between the parties. We show that the amount of violation of a Bell inequality imposes a lower bound on the average…
We consider general settings of Bell inequality experiments with many parties, where each party chooses from a finite number of measurement settings each with a finite number of outcomes. We investigate the constraints that Bell…
Bell's inequalities are defined by sums of correlations involving non-commuting observables in each of the two systems. Violations of Bell's inequalities are only possible because the precision of any joint measurement of these observables…
In quantum mechanics, nonlocality (a violation of a Bell inequality) is intimately linked to complementarity, by which we mean that consistently assigning values to different observables at the same time is not possible. Nonlocality can…
We report correlation measurements on two $^9$Be$^+$ ions that violate a chained Bell inequality obeyed by any local-realistic theory. The correlations can be modeled as derived from a mixture of a local-realistic probabilistic distribution…
What can be more fascinating than {\it experimental metaphysics}, to quote one of Abner Shimony's enlightening expressions? Bell inequalities are at the heart of the study of nonlocality. I present a list of open questions, organised in…
With Bell's inequalities one has a formal expression to show how essentially all local theories of natural phenomena that are formulated within the framework of realism may be tested using a simple experimental arrangement. For the case of…
Why do correlations between the results of measurements performed on physical systems violate Bell and non-contextuality inequalities up to some specific limits? The answer may follow from the observation that in quantum theory, unlike in…
Several authors have recently claimed that Bell's inequalities (BI) do not apply to certain types of generalized local hidden variables (HV) models. These claims are rejected, by means of a proof of BI valid for a very broad class of local…
The well known Bell experiment with two actors Alice and Bob is considered. First the simple deduction leading to the CHSH inequality under local realism is reviewed, and some arguments from the literature are recapitulated. Then I take up…
Bell inequalities may only be derived, if hidden variables do not depend on the experimental settings. The stochastic independence of hidden and setting variables is called: freedom of choice, free will, measurement independence or no…
It is demonstrated that hidden variables of a certain type follow logically from a certain local causality requirement (``Bell Locality'') and the empirically well-supported predictions of quantum theory for the standard EPR-Bell setup. The…
We emphasize the role of the precise correlations loophole in attempting to connect the CHSH type inequalities with the EPR-argument. The possibility to test theories with hidden variables experimentally by using such inequalities is…