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A Bell test can rule out local realistic models, and has potential applications in communications and information tasks. For example, a Bell inequality violation can certify the presence of intrinsic randomness in measurement outcomes,…

Bell's inequality was originally derived under the assumption that experimenters are free to select detector settings independently of any local "hidden variables" that might affect the outcomes of measurements on entangled particles. This…

The violation of Bell inequalities is often interpreted as showing that, if hidden variables exist, they must be contextual and non local. But they can also be explained questioning the probability space employed, or the validity of the…

This paper provides a systematic analysis of Bell experiments from the relational perspective, demonstrating that the apparent ``nonlocality'' of quantum mechanics stems from a problematic application of relativistic principles rather than…

In contrast to the wide-spread opinion that any separable quantum state satisfies every classical probabilistic constraint, we present a simple example where a separable quantum state does not satisfy the original Bell inequality although…

It is shown that the Bell inequalities are closely related to the triangle inequalities involving distance functions amongst pairs of random variables with values $\left\{ 0,1\right\} $. A hidden variables model may be defined as a mapping…

A proof of Bell's theorem without inequalities and involving only two observers is given by suitably extending a proof of the Bell-Kochen-Specker theorem due to Mermin. This proof is generalized to obtain an inequality-free proof of Bell's…

The majority of recent works investigating the link between non-locality and randomness, e.g. in the context of device-independent cryptography, do so with respect to some specific Bell inequality, usually the CHSH inequality. However, the…

The correlations that violate the CHSH inequality are known to have complementary contributions from signaling and local indeterminacy. This complementarity is shown to represent a strengthening of Bell's theorem, and can be used to certify…

In our contextual model, statistical independence is violated, thus it is not constrained by Bell Theorem. Individual outcomes are created locally in a deterministic way in a function of setting dependent variables describing measuring…

Many issues combine for consideration when speaking of Bell's Inequalities: nonlocality, realism, hidden variables, incompatible measures, wave function collapse, other. Each of these issues then may be viewed from several viewpoints:…

To date, most efforts to demonstrate quantum nonlocality have concentrated on systems of two (or very few) particles. It is however difficult in many experiments to address individual particles, making it hard to highlight the presence of…

Bell inequalities are a consequence of measurement incompatibility (not, as generally thought, of nonlocality). In classical terms, this is equivalent to contextuality -- measurement devices do have a significant effect. Contextual models…

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…

In a paper published in the journal Physics Essays in 2021, the author D.L. Mamas writes "A polarized photon interacts with a polarizer through the component of the photon's electric field which is aligned with the polarizer. This component…

Bell inequalities are an important tool in device-independent quantum information processing because their violation can serve as a certificate of relevant quantum properties. Probably the best known example of a Bell inequality is due to…

Marian Kupczynski(MK)is the author of a controversial paper published (2020) in the journal Frontiers in Physics. The work is built around a mathematical claim by MK which is actually false, and MK's logical reasoning around his claim is…

I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for…

The Nobel prize in physics for 2022 was given for performing Bell experiments with varying degree of sophistication. The interpretation of this experiment is discussed by first recalling Bell's simple argument behind his inequalities, in…

The Bell inequality is derived under the assumption of three physical data sets, random or deterministic. The data sets represent a laboratory realization of the three probability based variables used by Bell. For physical data as can be…