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Since the experimental observation of the violation of the Bell-CHSH inequalities, much has been said about the non-local and contextual character of the underlying system. But the hypothesis from which Bell's inequalities are derived…
Contextuality and entanglement are valuable resources for quantum computing and quantum information. Bell inequalities are used to certify entanglement; thus, it is important to understand why and how they are violated. Quantum mechanics…
Recently, a group of experiments tested local realism with random choices prepared by humans. These various tests were subject to additional assumptions, which lead to loopholes in the interpretations of almost all of the experiments. Among…
Theoretical considerations of Bell-inequality experiments usually assume identically prepared and independent pairs of particles. Here we consider pairs that exhibit both intra- and inter-pair entanglement. The pairs are taken from a large…
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…
Local realism is the worldview in which physical properties of objects exist independently of measurement and where physical influences cannot travel faster than the speed of light. Bell's theorem states that this worldview is incompatible…
In order to reject the local hidden variables hypothesis, the usefulness of a Bell inequality can be quantified by how small a p-value it will give for a physical experiment. Here we show that to obtain a small expected p-value it is…
Despite claims that Bell's inequalities are based on the Einstein locality condition, or equivalent, all derivations make an identical mathematical assumption: that local hidden-variable theories produce a set of positive-definite…
We derive two classes of multi-mode Bell inequalities under local realistic assumptions, which are violated only by the entangled states negative under partial transposition in accordance with the Peres conjecture. Remarkably, the failure…
Reviewing the general representation of a stochastic local hidden variables theory in the context of an ideal Bohm's version of the EPR experiment, we show explicitly that the violation of Bell's locality condition is due to the assumption…
It is generally believed that Bell's inequality holds for the case of entangled states, including two correlated particles or special states of a single particle. Here, we derive a single-particle Bell's inequality for two correlated spin…
It is demonstrated that hidden variables of a certain type follow logically from a certain local causality requirement (``Bell Locality'') and the empirically well-supported predictions of quantum theory for the standard EPR-Bell setup. The…
In the derivation of Bell's inequalities, probability distribution is supposed to be a function of only hidden variable. We point out that the true implication of the probability distribution of Bell's correlation function is the…
Bell gave the now standard definition of a local hidden variable theory and showed that such theories cannot reproduce the predictions of quantum mechanics without violating his ``free will'' criterion: experimenters' measurement choices…
In its vast majority entanglement verification is examined either in the complete characterized or totally device independent scenario. The assumptions imposed by these extreme cases are often either too weak or strong for real experiments.…
The Bell theorem is explored in terms of a trade-off relation between underlying assumptions within the hidden variable model framework. In this paper, recognizing the incorporation of hidden variables as one of the fundamental assumptions,…
Bell inequalities may only be derived, if hidden variables do not depend on the experimental settings. The stochastic independence of hidden and setting variables is called: freedom of choice, free will, measurement independence or no…
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…
We present a loophole-free violation of local realism using entangled photon pairs. We ensure that all relevant events in our Bell test are spacelike separated by placing the parties far enough apart and by using fast random number…
While initial versions of Bell's theorem captured the notion of locality with the assumption of factorizability, in later presentations, Bell argued that factorizability could be derived from the more fundamental principle of local…