Related papers: Separation theorems and Bell inequalities in algeb…

The assumptions required for the derivation of Bell inequalities are not usually satisfied for random fields in which there are any thermal or quantum fluctuations, in contrast to the general satisfaction of the assumptions for classical…

We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical…

In the first part of this thesis Bell's theorem is revisited. It points at a difference between the quantum and the classical world. This difference is often behind the advantages of solutions using quantum mechanics. New and more general…

Based on a geometrical argument introduced by Zukowski, a new multisetting Bell inequality is derived, for the scenario in which many parties make measurements on two-level systems. This generalizes and unifies some previous results.…

Bell inequalities are a consequence of measurement incompatibility (not, as generally thought, of nonlocality). In classical terms, this is equivalent to contextuality -- measurement devices do have a significant effect. Contextual models…

The derivation of Bell inequalities in terms of quantum statistical (thermodynamic) entropies is considered. Inequalities of the Wigner form are derived but shown to be extremely limiting in their applicability due to the nature of the…

For an N-partite quantum system we show that separability implies inequalities on Bell correlations which are stronger than the local reality inequalities by a factor 2^{(N-1)/2}.

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 discuss the recently observed "loophole free" violation of Bell's inequalities in the framework of a physically realist view of quantum mechanics, which requires that physical properties are attributed jointly to a system, and to the…

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…

Bell-inequality violations reveal the presence of quantum correlations between two particles that have interacted and then separated. Their generalisation to quantum fields is necessary to study a number of field-theoretic setups, such as…

Quantum entanglement describes superposition states in multi-dimensional systems, at least two partite, which cannot be factorized and are thus non-separable. Non-separable states exist also in classical theories involving vector spaces. In…

We establish new metric characterizations for the norm (respectively, ultraweak) closure of the convex hull of a bounded set in an arbitrary $C^*$-algebra (respectively, von Neumann algebra), and provide applications of these results to the…

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].…

This text is an introduction to an operational outlook on Bell inequalities, which has been very fruitful in the past few years. It has lead to the recognition that Bell tests have their own place in applied quantum technologies, because…

Bell's theorem supposedly demonstrates an irreconcilable conflict between quantum mechanics and local, realistic hidden variable theories. Most proofs of Bell's theorem, are based on inequalities. In this paper we present an alternative…

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…

We define quantum-like probabilistic behaviour as behaviour which is impossible to describe by using the classical probability model. We discuss the conjecture that cognitive behaviour is quantum-like. There is presented the scheme for an…

It is not generally known, that the inequality that Bell derived using three random variables must be identically satisfied by any three corresponding data sets of plus and minus 1s that are writable on paper.This surprising fact is not…

We present tight Bell inequalities expressed by probabilities for three four- and five-dimensional systems. The tight structure of Bell inequalities for three $d$-dimensional systems (qudits) is proposed. Some interesting Bell inequalities…