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It is argued that local realism is a fundamental principle, which might be rejected only if experiments clearly show that it is untenable. A critical review is presented of the derivations of Bell's inequalities and the performed…

We propose to detect quantum entanglement by a condition of local measurments. We find that this condition can detect efficiently the pure entangled states for both discrete and continuous variable systems. It does not depend on…

Proposals for Bell inequality tests on systems restricted by superselection rules often require operations that are difficult to implement in practice. In this paper, we derive a new Bell inequality, where pairs of states are used to…

Bell's theorem supposedly demonstrates an irreconcilable conflict between quantum mechanics and local, realistic hidden variable theories. In this paper we show that all experiments that aim to prove Bell's theorem do not actually achieve…

Quantum theory is inconsistent with any local hidden variable model as was first shown by Bell. To test Bell inequalities two separated observers extract correlations from a common ensemble of identical systems. Since quantum theory does…

We have experimentally tested the non local properties of the states generated by a high brilliance source of entanglement which virtually allows the direct measurement of the full set of photon pairs created by the basic QED process…

While all bipartite pure entangled states are known to generate correlations violating a Bell inequality, and are therefore nonlocal, the quantitative relation between pure-state entanglement and nonlocality is poorly understood. In fact,…

Recently an alternative way to quantify Bell nonlocality has been proposed [Phys. Rev. A {\bf 92}, 030101(R) (2015)]. In this work we further develop this concept, the volume of violation, and analytically calculate its value for the…

The predictions of local realistic theories for the observables concerning the evolution of a $K^0\bar{K}^0$ quantum entangled pair (created in the decay of the $\phi$-meson) are discussed. It is shown, in agreement with Bell's theorem,…

We describe a new Bell test for two-particle entangled systems that engages an unbounded continuous variable. The continuous variable state is allowed to be arbitrary and inaccessible to direct measurements. A systematic method is…

Bell inequalities reveal the fundamentally nonlocal character of quantum mechanics. In this regard, one of the interesting problems is to explore all possible Bell inequalities that demonstrate a gap between local and nonlocal quantum…

Tests of local realism and their applications aim for very high confidence in their results even in the presence of potentially adversarial effects. For this purpose, one can measure a quantity that reflects the amount of violation of local…

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…

The essence of Bell's theorem is that, in general, quantum statistics cannot be reproduced by local hidden variable (LHV) model. This impossibility is strongly manifested while analyzing the singlet state statistics for Bell-CHSH…

So far, various Bell type inequalities have been introduced to test the local realism in tripartite systems. In this article we consider a tripartite system with two measurements in each side and two outputs for each measurement. Then we…

Hardy's nonlocality argument, which establishes incompatibility of quantum theory with local-realism, can also be used to reveal the time-nonlocal feature of quantum states. For spin-1/2 systems, the maximum probability of success of this…

A recent experiment reported the first violation of a Bell correlation witness in a many-body system [Science 352, 441 (2016)]. Following discussions in this paper, we address here the question of the statistics required to witness Bell…

The violation of Bell inequalities where both detection and locality loopholes are closed is crucial for device independent assessments of quantum information. While of technological nature, the simultaneous closing of both loopholes still…

We propose a new method for detecting entanglement of two qubits and discuss its relation with the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality. Without the need for full quantum tomography for the density matrix we can experimentally…

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…