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A Bell test can rule out local realistic models, and has potential applications in communications and information tasks. For example, a Bell inequality violation can certify the presence of intrinsic randomness in measurement outcomes,…
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…
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…
Three classes of local hidden-variable models that violate both Bell and Leggett inequalities are presented. The models, however, do not reproduce the quantum mechanical predictions, hence they are experimentally testable. It is concluded…
Bell inequalities were meant to test quantum mechanics vs local hidden variable models, but can also be used to verify entanglement. For entanglement verification purposes one assumes the validity of quantum mechanics as well as quantum…
A continuous-variable Bell inequality, valid for an arbitrary number of observers measuring observables with an arbitrary number of outcomes, was recently introduced in [Cavalcanti \emph{et al.}, Phys. Rev. Lett. {\bf 99}, 210405 (2007)].…
A simple local hidden-variables model is exhibited which reproduces the results of all performed tests of Bell\'{}s inequalities involving optical photon pairs. For the old atomic-cascade experiments, like Aspect\'{}s, the model agrees with…
Explicit local hidden variables models are exhibited that assume a correlation between detection events produced in the same detector at different times. It is shown that some models give predictions closer to the Bell limit than models…
Bell inequalities are mathematical constructs that demarcate the boundary between quantum and classical physics. A new class of multiplicative Bell inequalities originating from a volume maximization game (based on products of correlators…
We introduce Bell-type inequalities allowing for non-locality and entanglement tests with two cold heteronuclear molecules. The proposed inequalities are based on correlations between each molecule spatial orientation, an observable which…
On one side, so far a great part of the evidence accepted as proof of the alleged quantum non-locality relied on inhomogeneous Bell inequalities involving an additional assumption (no-enhancement) whose role had not been sufficiently…
We analyze and compare the mathematical formulations of the criterion for separability for bipartite density matrices and the Bell inequalities. We show that a violation of a Bell inequality can formally be expressed as a witness for…
The question has been solved whether Bell's inequalities cover all possible kinds of hidden-variable theories. It has been shown that the given nequalities can be hardly derived when the changing space position of photon-pair source…
It is shown that the Bell inequalities are closely related to the triangle inequalities involving distance functions amongst pairs of random variables with values $\left\{ 0,1\right\} $. A hidden variables model may be defined as a mapping…
The predictions of quantum mechanics cannot be resolved with a completely classical view of the world. In particular, the statistics of space-like separated measurements on entangled quantum systems violate a Bell inequality. We put forward…
Bell inequalities rely on an assumption that the probabilities of adopting configurations of hidden variables describing a system prior to measurement are independent of the choice of measured physical property, also known as measurement…
Characterizing the set of all Bell inequalities is a notably hard task. An insightful method of solving it in case of Bell correlation inequalities for scenarios with two dichotomic measurements per site - for arbitrary number of parties -…
We consider bipartite quantum systems characterized by a continuous angular variable \theta \in [-\pi, \pi[, representing, for instance, the position of a particle on a circle. We show how to reveal non-locality on this type of system using…
As discussed below, Bell's inequalities and experimental results rule out commutative hidden variable models as a basis for Bell correlations, but not necessarily non-commutative probability models. A local probability model is constructed…
It is generally believed that Bell's inequality holds for the case of entangled states, including two correlated particles or special states of a single particle. Here, we derive a single-particle Bell's inequality for two correlated spin…