Related papers: George Boole and the Bell inequalities
Classical Pitowsky correlation polytopes are reviewed with particular emphasis on the Minkowski-Weyl representation theorem. The inequalities representing the faces of polytopes are Boole's ``conditions of possible experience.'' Many of…
This article contains a review of Nelson's analysis of Bell's theorem. It shows that Bell's inequalities can be violated with a theory of local random variables if one accepts that the outcomes of these variables are not predetermined prior…
Physical principles constraints the way nonlocal correlations can be distributed among distant parties in a Bell-type experiment. These constraints are usually expressed by monogamy relations that bound the amount of Bell inequality…
We present an analysis of the structure of Bell inequalities, mainly for the case of N qubits with two observables each. We show that these inequalities are related to Hadamard matrices and define Bell polynomials (in one variable) as an…
The recently proposed (Phys. Rev. A90 (2014), 062121 and Phys. Rev. A91 (2015), 052110) group theoretical approach to the problem of breaking the Bell inequalities is applied to $S_4$ group. The Bell inequalities based on the choice of…
The correspondence principle suggests that quantum systems grow classical when large. Classical systems cannot violate Bell inequalities. Yet agents given substantial control can violate Bell inequalities proven for large-scale systems. We…
According to recent reports, the last loopholes in testing Bell's inequality are closed. It is argued that the really important task in this field has not been tackled yet and that the leading experiments claiming to close locality and…
Bell inequalities are important tools in contrasting classical and quantum behaviors. To date, most Bell inequalities are linear combinations of statistical correlations between remote parties. Nevertheless, finding the classical and…
Bell inequalities applicable to non-ideal EPRB experiments are critical to the interpretation of experimental Bell tests. In this article it is shown that previous treatments of this subject are incorrect due to an implicit assumption and…
In constructing his theorem, Bell assumed that correlation functions among non-commuting variables are the same as those among commuting variables. However, in quantum mechanics, multiple data values exist simultaneously for commuting…
We show that Bell inequalities can be violated in the macroscopic world. The macroworld violation is illustrated using an example involving connected vessels of water. We show that whether the violation of inequalities occurs in the…
We established a physically utilizable Bell inequality based on the Peres-Horodecki criterion. The new quadratic probabilistic Bell inequality naturally provides us a necessary and sufficient way to test all entangled two-qubit or…
The difference between ideal experiments to test Bell's weak nonlocality and the real experiments leads to loopholes. Ideal experiments involve either inequalities (Bell) or equalities (Greenberger, Horne, Zeilinger). Every real experiment…
A logical approach to Bell's Inequalities of quantum mechanics has been introduced by Abramsky and Hardy [2]. We point out that the logical Bell's Inequalities of [2] are provable in the probability logic of Fagin, Halpern and Megiddo [4].…
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…
Bell tests---the experimental demonstration of a Bell inequality violation---are central to understanding the foundations of quantum mechanics, underpin quantum technologies, and are a powerful diagnostic tool for technological developments…
In 1976, I met John Bell several times in CERN and we talked about a possible violation of optical theorem, purity tests, EPR paradox, Bell inequalities and their violation. I review our discussions, and explain how they were related to my…
John Bell is generally credited to have accomplished the remarkable "proof" that any theory of physics, which is both Einstein-local and "realistic" (counterfactually definite), results in a strong upper bound to the correlations that are…
Bell inequalities are intended to show that local realist theories cannot describe the world. A local realist theory is one where physical properties are defined prior to and independent of measurement, and no physical influence can…
Specification of the strongest possible Bell inequalities for arbitrarily complicated physical scenarios -- any number of observers choosing between any number of observables with any number of possible outcomes -- is currently an open…