Related papers: Multideviations: The hidden structure of Bell's th…
We explore the challenges posed by the violation of Bell-like inequalities by $d$-dimensional systems exposed to imperfect state-preparation and measurement settings. We address, in particular, the limit of high-dimensional systems,…
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…
The fields of quantum non-locality in physics, and causal discovery in machine learning, both face the problem of deciding whether observed data is compatible with a presumed causal relationship between the variables (for example a local…
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 first part of this paper contains an introduction to Bell inequalities and Tsirelson's theorem for the non-specialist. The next part gives an explicit optimum construction for the "hard" part of Tsirelson's theorem. In the final part we…
Bell inequalities bound the strength of classical correlations between observers measuring on a shared physical system. However, studies of physical correlations can be considered beyond the standard Bell scenario by networks of observers…
There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…
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…
Entanglement and its consequences - in particular the violation of Bell inequalities, which defies our concepts of realism and locality - have been proven to play key roles in Nature by many experiments for various quantum systems.…
While the interest in multipartite nonlocality has grown in recent years, its existence in large quantum systems is difficult to confirm experimentally. This is mostly due to the inadequacy of standard multipartite Bell inequalities to…
Bell inequalities are natural tools that allow one to certify the presence of nonlocality in quantum systems. The known constructions of multipartite Bell inequalities contain, however, correlation functions involving all observers, making…
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…
It is shown that Bell's counterfactuals admit joint quasiprobability distributions (i.e. joint distributions exist, but may not be non-negative). A necessary and sufficient condition for the existence among them of a true probability…
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 inequalities or Bell-like experiments are supposed to test hidden variable theories based on three intuitive assumptions: determinism, locality and measurement independence. If one of the assumptions of Bell inequality is properly…
We derive tight quadratic inequalities for all kinds of hybrid separable-inseparable $n$-particle density operators on an arbitrary dimensional space. This methodology enables us to truly derive a tight quadratic inequality as tests for…
We present generic Bell inequalities for multipartite multi-dimensional systems. The inequalities that any local realistic theories must obey are violated by quantum mechanics for even-dimensional multipartite systems. A large set of…
The Bell inequalities in three and four correlations are re-derived in general forms showing that three and four data sets, respectively, identically satisfy them regardless of whether they are random, deterministic, measured, predicted, or…
We derive tight Bell's inequalities for N>2 observers involving more than two alternative measurement settings. We give a necessary and sufficient condition for a general quantum state to violate the new inequalities. The inequalities are…
Initially motivated by their relevance in foundations of quantum mechanics and more recently by their applications in different contexts of quantum information science, violations of Bell inequalities have been extensively studied during…