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Nonlocality, manifested by the violation of Bell inequalities, indicates entanglement within a joint quantum system. A natural question is how much entanglement is required for a given nonlocal behavior. Here, we explore this question by…

Hardy's nonlocality is a "nonlocality proof without inequalities": it exemplifies that quantum correlations can be qualitatively stronger than classical correlations. This paper introduces variants of Hardy's nonlocality in the CHSH…

Based on the new general framework for the probabilistic description of experiments, introduced in quant-ph/0305126, quant-ph/0312199, we analyze in mathematical terms the link between the validity of Bell-type inequalities under joint…

Quantum nonlocality concerns correlations among spatially separated systems that cannot be classically explained without post-measurement communication among the parties. Thus, a natural measure of nonlocal correlations is provided by the…

There exist numerous proofs of Bell's theorem, stating that quantum mechanics is incompatible with local realistic theories of nature. Here we define the strength of such nonlocality proofs in terms of the amount of evidence against local…

Bell's theorem has been widely argued to show that some of the predictions of quantum mechanics which are obtained by applying the {\it Born's rule} to a class of {\it entangled states}, are {\it not} compatible with {\it any} local-causal…

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.…

One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…

Given a pair of isolated devices that accept random binary inputs and return binary outputs, a user can deduce from the observed data alone if the underlying mechanism can be explained classically. Bell's theorem further states that a…

Bell nonlocality and Kochen-Specker contextuality are two remarkable nonclassical features of quantum theory, related to strong correlations between outcomes of measurements performed on quantum systems. Both phenomena can be witnessed by…

Many solid-state quantum platforms do not permit sharp, projective measurements but instead yield continuous voltage or field traces under weak, non-demolition readout. In such systems, standard Bell tests based on dichotomic projective…

Bell's theorem is 50 years old. Still there is a controversy about its implications. Much of it has its roots in confusion regarding the premises from which the theorem can be derived. Some claim that a derivation of Bell's inequalities…

Nonlocality and quantum entanglement constitute two special aspects of the quantum correlations existing in quantum systems, which are of paramount importance in quantum-information theory. Traditionally, they have been regarded as…

Bell nonlocality plays a fundamental role in quantum theory. Numerous tests of the Bell inequality have been reported since the ground-breaking discovery of the Bell theorem.Up to now, however, most discussions of the Bell scenario have…

Non-classical probability is the underlying feature of quantum mechanics. The emergence of Bell-CHSH non-locality for bipartite systems and linear entanglement inequalities for two-qubit systems has been shown in Adhikary et al. 2020 [Eur.…

We propose a scheme to test Bell's inequalities for an arbitrary number of measurement outcomes on entangled continuous variable states. The Bell correlation functions are expressible in terms of phase-space quasiprobability functions with…

In his article in Science, Nicolas Gisin claimed that quantum correlations emerge from outside space time. We explain that they are due to space time symmetries. This paper is a critical review of metaphysical conclusions found in many…

A continuous-variable Bell inequality, valid for an arbitrary number of observers measuring observables with an arbitrary number of outcomes, was recently introduced in [Cavalcanti \emph{et al.}, Phys. Rev. Lett. {\bf 99}, 210405 (2007)].…

In a Bell test, the set of observed probability distributions complying with the principle of local realism is fully characterized by Bell inequalities. Quantum theory allows for a violation of these inequalities, which is famously regarded…

We show that for two-qubit chained Bell inequalities with an arbitrary number of measurement settings, nonlocality and entanglement are not only different properties but are inversely related. Specifically, we analytically prove that in…