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We detail and extend the results of [Milman {\it et al.}, Phys. Rev. Lett. {\bf 99}, 130405 (2007)] on Bell-type inequalities based on correlations between measurements of continuous observables performed on trapped molecular systems. We…

Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order…

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…

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…

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…

Bell nonlocality refers to correlations between two distant, entangled particles that challenge classical notions of local causality. Beyond its foundational significance, nonlocality is crucial for device-independent technologies like…

We propose a method to generate analytical quantum Bell inequalities based on the principle of Macroscopic Locality. By imposing locality over binary processings of virtual macroscopic intensities, we establish a correspondence between Bell…

The use of Bell's theorem in any application or experiment relies on the assumption of free choice or, more precisely, measurement independence, meaning that the measurements can be chosen freely. Here, we prove that even in the simplest…

Any physical theory aims to establish the relationship between physical systems in terms of the interaction between these systems. However, any known approach in the literature to infer this interaction is dependent on the particular…

Quantum nonlocality is presented often as the most remarkable and inexplicable phenomenon known to modern science which was confirmed in the experiments proving the violation of Bell Inequalities (BI). It has been known already for a long…

Bell's theorem basically states that local hidden variable theory cannot predict the correlations produced by quantum mechanics. It is based on the assumption that Alice and Bob can choose measurements from a measurement set containing…

For a system composed of two particles Bell's theorem asserts that averages of physical quantities determined from local variables must conform to a family of inequalities. In this work we show that a classical model containing a local…

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…

Quantum theory predicts and experiments confirm that nature can produce correlations between distant events that are nonlocal in the sense of violating a Bell inequality. Nevertheless, Bell's strong sentence {\it Correlations cry out for…

Some temporal Bell inequalities are deduced under the assumption of realism and perfect correlation. No locality condition is needed. When the system is macroscopic, the perfect correlation assumption substitutes the noninvasive…

The experimentally verified violation of Bell's inequalities apparently implies that at least one of two intuitive beliefs must be false: that effects propagating at infinite velocity do not exist, and that natural phenomena occur…

This paper illustrates a direct connection between quantum steering and non-trivial preparation contextuality. In two party-two measurement per party-two outcomes per measurement $(2-2-2)$ Bell scenario, any argument of Bell nonlocality is…

The paper deals with conditional linear information inequalities valid for entropy functions induced by discrete random variables. Specifically, the so-called conditional Ingleton inequalities are in the center of interest: these are valid…

We take a resource-theoretic approach to the problem of quantifying nonclassicality in Bell scenarios. The resources are conceptualized as probabilistic processes from the setting variables to the outcome variables having a particular…