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In contrast with classical physics, in quantum physics some sets of measurements are incompatible in the sense that they can not be performed simultaneously. Among other applications, incompatibility allows for contextuality and Bell…

Besides well-known conditions of locality or factorisability, deriving the Bell inequalities requires assuming that the distribution of hidden variables and Alice's and Bob's measurement settings be independent of each other. We show that…

Quantum theory allows for nonlocality without entanglement. Notably, there exist bipartite quantum measurements consisting of only product eigenstates, yet they cannot be implemented via local quantum operations and classical communication.…

Based on the optimal quantum violation of suitable Bell's inequality, the device-independent self-testing of state and observables has been reported. It is well-studied that locally commuting or compatible observables cannot be used to…

According to Bell's theorem, local realism is incompatible with quantum theory. However, it depends on an implied assumption about quantum measurement. We suggest that the assumption might be removed by a detailed quantum analysis of the…

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…

The Bell inequality is thought to be a common constraint shared by all models of local hidden variables that aim to describe the entangled states of two qubits. Since the inequality is violated by the quantum mechanical description of these…

This paper is aimed to dissociate nonlocality from quantum theory. We demonstrate that the tests on violation of the Bell type inequalities are simply statistical tests of local incompatibility of observables. In fact, these are tests on…

In this Comment we show that Cabello's argument [Phys. Rev. Lett. 86, 1911 (2001)] which proves the nonlocal feature of any classical model of quantum mechanics based on Einstein-Podolsky-Rosen (EPR) criterion of elements of reality, must…

It is well known that jointly measurable observables cannot lead to a violation of any Bell inequality - independent of the state and the measurements chosen at the other site. In this letter we prove the converse: every pair of…

Relevant aspects for testing Bell inequalities with entangled meson-antimeson systems are analyzed. In particular, we argue that the result of A. Go, J. Mod. Optics 51, 991 (2004), which nicely illustrate the quantum entanglement of B-meson…

Bell's theorem supposedly demonstrates an irreconcilable conflict between quantum mechanics and local, realistic hidden variable theories. Most proofs of Bell's theorem, are based on inequalities. In this paper we present an alternative…

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…

We observe strong violation of Bell's inequality in an Einstein, Podolsky and Rosen type experiment with independent observers. Our experiment definitely implements the ideas behind the well known work by Aspect et al. We for the first time…

We show that rejection of local realism in quantum mechanics can be tested by Bell-type inequalities for two observers and low-order moments of continuous and unbounded observables. We prove that one requires three observables for each…

One of the most notable aspects of quantum systems is that their components can exhibit correlations much stronger than those allowed by classical physics. Two examples of quantum correlations are quantum entanglement and Bell nonlocality,…

This article contains a review of Nelson's analysis of Bell's theorem. It shows that Bell's inequalities can be violated with a theory of local random variables if one accepts that the outcomes of these variables are not predetermined prior…

We use a local theory of photons purely as particles to model the single-photon experiment proposed by Tan, Walls, and Collett. Like Tan et al. we are able to derive a violation of Bell's inequalities for photon counts coincidence…

Recently there has been an increased interest in possible tests of locality via Bell's inequality or tests of entanglement at colliders, in particular at the LHC. These have involved various physical processes, such as $t \bar t$, or…

Incompatible measurements, i.e., measurements that cannot be simultaneously performed, are necessary to observe nonlocal correlations. It is natural to ask, e.g., how incompatible the measurements have to be to achieve a certain violation…