Related papers: Bell's Inequality, Causal Bounds, and Quantum Baye…
Since the experimental observation of the violation of the Bell-CHSH inequalities, much has been said about the non-local and contextual character of the underlying system. But the hypothesis from which Bell's inequalities are derived…
Non-classical quantum correlations underpin both the foundations of quantum mechanics and modern quantum technologies. Among them, Bell nonlocality is a central example. For bipartite Bell inequalities, nonlocal correlations obey strict…
Einstein, Podolsky and Rosen (EPR) showed that it is possible to predict with certainty the value of a property without disturbing the object in question. In contrast, Quantum Mechanics (QM) holds that if different measurement setups cannot…
Instrumental variables allow the estimation of cause and effect relations even in presence of unobserved latent factors, thus providing a powerful tool for any science wherein causal inference plays an important role. More recently, the…
It is well-known that in a Bell experiment, the observed correlation between measurement outcomes -- as predicted by quantum theory -- can be stronger than that allowed by local causality, yet not fully constrained by the principle of…
Information causality was proposed as a physical principle to put upper bound on the accessible information gain in a physical bi-partite communication scheme. Intuitively, the information gain cannot be larger than the amount of classical…
The characterization of the set of quantum correlations is a problem of fundamental importance in quantum information. The question whether every proper (tight) Bell inequality is violated in Quantum theory is an intriguing one in this…
We present bipartite Bell-type inequalities which allow the two partners to use some non-local resource. Such inequality can only be violated if the parties use a resource which is more non-local than the one permitted by the inequality. We…
When three or more particles are considered, quantum correlations can be stronger than the correlations generated by so-called hybrid local hidden variable models, where some of the particles are considered as a single block inside which…
Bell's theorem of 1965 is a proof that all realistic interpretations of quantum mechanics must be non-local. Bell's theorem consists of two parts: first a correlation inequality is derived that must be satisfied by all local realistic…
Simple quantitative measures of indeterminism and signalling, $I$ and $S$, are defined for models of statistical correlations. It is shown that any such model satisfies a generalised Bell-type inequality, with tight upper bound B(I,S). This…
We point out that, when the dimension of the Hilbert space is greater than two, Bell's operators entering the Bell-CHSH inequality exhibit unitarily inequivalent representations. Although the Bell-CHSH inequality turns out to be violated,…
Quantum theory is in principle compatible with processes that violate causal inequalities, an analogue of Bell inequalities that constrain the correlations observed by sets of parties operating in a definite causal order. Since the…
The famous Clauser-Horne-Shimony-Holt (CHSH) inequality certifies a quantum violation, by a factor $\sqrt{2}$, of correlations predicted by the classical view of the world in the simplest possible nontrivial measurement setup (two systems…
Bell's theorem is a fundamental theorem in physics concerning the incompatibility between some correlations predicted by quantum theory and a large class of physical theories. In this paper, we introduce the hypothesis of accountability,…
Bell inequality violation is one of the most widely known manifestations of entanglement in quantum mechanics; indicating that experiments on physically separated quantum mechanical systems cannot be given a local realistic description.…
Nonlocality is one of the key features of quantum physics, which is revealed through the violation of a Bell inequality. In large multipartite systems, nonlocality characterization quickly becomes a challenging task. A common practice is to…
According to the Bell theorem, local hidden variable theories cannot reproduce all the predictions of quantum mechanics. An important consequence is that under physically reasonable assumptions quantum mechanics predicts correlations that…
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…
Nonlocality shapes quantum correlations, revealed through the violation of Bell inequalities. The intersection of all valid Bell inequalities is the so-called local polytope. In multipartite systems, characterizing the local polytope…