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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…

Bell tests---the experimental demonstration of a Bell inequality violation---are central to understanding the foundations of quantum mechanics, underpin quantum technologies, and are a powerful diagnostic tool for technological developments…

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…

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…

In this work we aim to analyze the Clauser-Horne-Shimony-Holt CHSH inequality strictly in the context of probability theory. In the course of assembling inequality we have to take care not to produce assumptions a priori, that is,…

The violation of a Bell inequality is an experimental observation that forces one to abandon a local realistic worldview, namely, one in which physical properties are (probabilistically) defined prior to and independent of measurement and…

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…

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…

Measurement incompatibility and quantum non-locality are two key features of quantum theory. Violations of Bell inequalities require quantum entanglement and incompatibility of the measurements used by the two parties involved in the…

The Bell and the Clauser-Horne-Shimony-Holt inequalities are shown to hold for both the cases of complex and real analytic nonlocality in the setting parameters of Einstein-Podolsky-Rosen-Bohm experiments for spin 1/2 particles and photons,…

The widespread claim that violations of Bell inequalities establish the nonlocality of nature is critically reexamined. It is argued that this conclusion is not logically compelled by either the Einstein-Podolsky-Rosen (EPR) argument or…

In a recent paper [T. C. Ralph, W. J. Munro, R. E. S. Polkinghorne, Phys. Rev. Lett. 85, 2035 (2000)], the authors propose a test for Bell's inequalities based on quadrature measurements for a correlated parametric source. We present here a…

Bell inequalities rely on an assumption that the probabilities of adopting configurations of hidden variables describing a system prior to measurement are independent of the choice of measured physical property, also known as measurement…

We consider typical experiments that use Bell-inequalities to test local-realist theories of quantum mechanics and gain insight into how certain results can be obtained. We see that results against local-realism arise from some `quantum…

Bell inequalities are intended to show that local realist theories cannot describe the world. A local realist theory is one where physical properties are defined prior to and independent of measurement, and no physical influence can…

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…

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…

Bell's inequality is derived from three assumptions: measurement independence, outcome independence, and parameter independence. Among these, measurement independence, often taken for granted, holds that hidden variables are statistically…

All previous tests of local realism have studied correlations between single-particle measurements. In the present experiment, we have performed a Bell experiment on three particles in which one of the measurements corresponds to a…

Recently Wang et al. have reported a violation of a Bell inequality without entanglement [arXiv:2507.07756]. We show that their result is an artifact of postselection. It is well known that postselection may yield Bell inequality…