Related papers: Determination of hidden variable models reproducin…
Recent experiments of Groeblacher et al. proved the violation of a Leggett-type inequality that was claimed to be valid for a broad class of non-local hidden-variable theories. The impossibility of constructing a non-local and realistic…
Bell's seminal work showed that no local hidden variable (LHV) model can fully reproduce the quantum correlations of a two-qubit singlet state. His argument and later developments by Clauser et al. effectively rely on gaps between the…
Whether the quantum mechanics (QM) is non-local is an issue disputed for a long time. The violation of the Bell-type inequalities was considered as proving this non-locality. However, these inequalities are constructed on a class of local…
The aim of this paper is to argue that the (alleged) indeterminism of quantum mechanics, claimed by adherents of the Copenhagen interpretation since Born (1926), can be proved from Chaitin's follow-up to Goedel's (first) incompleteness…
We present a simple hidden variable model for the singlet state of a pair of qubits, characterized by two kinds, hierarchically ordered, of hidden variables. We prove that, averaging over both types of variables, one reproduces all the…
The empirical proof of Bell inequality violations was a landmark moment for research into quantum foundations. It commits us to a universe without strict relativistic locality or requires that we escape through a potential loophole like…
Entanglement is one of the most intriguing features of quantum mechanics. It gives rise to peculiar correlations which cannot be reproduced by a large class of alternative theories, the so-called hidden-variable models, that use parameters…
With the advent of quantum information, the violation of a Bell inequality is used as evidence of the absence of an eavesdropper in cryptographic scenarios such as key distribution and randomness expansion. One of the key assumptions of…
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…
Bell's Theorem requires any theory which obeys the technical definitions of Free Choice and Local Causality to satisfy the Bell inequality. Invariant set theory is a finite theory of quantum physics which violates the Bell inequality…
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…
Bell derived the given inequalities on the basis of one rather forceful assumption that was supposed to hold in the hidden variable theory. However, this assumption has been so strong that it has corresponded only to the classical physics;…
In constructing his theorem, Bell assumed that correlation functions among non-commuting variables are the same as those among commuting variables. However, in quantum mechanics, multiple data values exist simultaneously for commuting…
In this paper we consider the description by a general Bell-type non-local hidden variable theory (NLHVT) of bipartite quantum states with two observables per sub-system. We derive Bell inequalities of the…
We remind the viewpoint that violation of Bell's inequality might be interpreted not only as an evidence of the alternative -- either nonlocality or ``death of reality'' (under the assumption the quantum mechanics is incomplete). Violation…
Many widely studied graphical models with latent variables lead to nontrivial constraints on the distribution of the observed variables. Inspired by the Bell inequalities in quantum mechanics, we refer to any linear inequality whose…
The observation of quantum nonlocality, i.e. quantum correlations violating a Bell inequality, implies the use of incompatible local quantum measurements. Here we consider the converse question. That is, can any set of incompatible…
Local hidden-variable model of singlet-state correlations discussed in M. Czachor, Arithmetic loophole in Bell's Theorem: Overlooked threat to entangled-state quantum cryptography, Acta Phys. Polon. A 139, 70-83 (2021), is shown to be a…
The discussion of the foundations of quantum mechanics is complicated by the fact that a number of different issues are closely entangled. Three of these issues are i) the interpretation of probability, ii) the choice between realist and…
A new pure quantum state, isotropic in spin variables, is defined in an extended spin phase space beyond standard quantum mechanics. It allows to represent the entangled singlet state in separable form. The statistical correlations between…