Related papers: Separation theorems and Bell inequalities in algeb…
We provide an overview of the connections between Bell's inequalities and algebraic structure.
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…
This short article concentrates on the conceptual aspects of the violation of Bell inequalities, and acts as a map to the 265 cited references. The article outlines (a) relevant characteristics of quantum mechanics, such as statistical…
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…
A new interpretation offers a consistent conceptual basis for nonrelativistic quantum mechanics. The violation of Bell's inequality is explained by maintaining realism, inductive inference and Einstein separability.
Understanding the limits of quantum theory in terms of uncertainty and correlation has always been a topic of foundational interest. Surprisingly this pursuit can also bear interesting applications such as device-independent quantum…
Bell inequalities, understood as constraints between classical conditional probabilities, can be derived from a set of assumptions representing a common causal explanation of classical correlations. A similar derivation, however, is not…
We will demonstrate in this paper that Bell's theorem (Bell's inequality) does not really conflict with quantum mechanics, the controversy between them originates from the different definitions for the expectation value using the…
We provide a framework for Bell inequalities which is based on multilinear contractions. The derivation of the inequalities allows for an intuitive geometric depiction and their violation within quantum mechanics can be seen as a direct…
Many issues combine for consideration when speaking of Bell's Inequalities: nonlocality, realism, hidden variables, incompatible measures, wave function collapse, other. Each of these issues then may be viewed from several viewpoints:…
Bell's theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of pre-existing local properties. We give an…
The relations between Bell's inequality and quantum probability trees are explained against the background offered by the concept of a quantum probability tree built in others works. It is shown that f we use a concept of probability tree…
We introduce two types of statistical quasi-separation between local observables to construct two-party Bell-type inequalities for an arbitrary dimensional systems and arbitrary number of measurement settings per site. Note that, the main…
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
It is argued that the lesson we should learn from Bell's inequalities is not that quantum mechanics requires some kind of action at a distance, but that it leads us to believe in parallel worlds.
A set of Bell inequalities classifying the quantum entanglement of four-qubit states is presented. These inequalities involve only two measurement settings per observer and can characterize fully separable, bi-separable and tri-separable…
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…
Over the past few decades, experimental tests of Bell-type inequalities have been at the forefront of understanding quantum mechanics and its implications. These strong bounds on specific measurements on a physical system originate from…
Bell's inequalities in the form given by Wigner are derived from the so-called fundamental assumption of statistical mechanics. I then demonstrate the possible relationship between these inequalities and the second law, particularly if…
We discuss general Bell inequalities for bipartite and multipartite systems, emphasizing the connection with convex geometry on the mathematical side, and the communication aspects on the physical side. Known results on families of…