Related papers: Model-free inequality for data of Einstein-Podolsk…
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…
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…
John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued…
We describe a simple experimental setting where joint measurements performed on a single (classical or quantum) entity can violate both the Bell-CHSH inequality and the marginal laws (also called no-signaling conditions). Once emitted by a…
We analyse the proof of Bell's inequality and demonstrate that this inequality is related to one particular model of probability theory, namely Kolmogorov measure-theoretical axiomatics, 1933. We found a (numerical) statistical correction…
Some temporal Bell inequalities are deduced under the assumption of realism and perfect correlation. No locality condition is needed. When the system is macroscopic, the perfect correlation assumption substitutes the noninvasive…
A direct analysis of the protocol of randomness amplification using Bell inequality violation is performed in terms of the convex combination of no-signaling boxes required to simulate quantum violation of the inequality. The probability…
Bell's theorem sets a boundary between the classical and quantum realms, by providing a strict proof of the existence of entangled quantum states with no classical counterpart. An experimental violation of Bell's inequality demands…
Quantum correlations that violate the Bell inequality cannot be explained by any (measurement independent) local hidden variable theory. However, the violation only implies incompatibility of the underlying assumptions of reality, locality,…
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…
Bell inequalities bound the strength of classical correlations between observers measuring on a shared physical system. However, studies of physical correlations can be considered beyond the standard Bell scenario by networks of observers…
We show how the Bell correlations can be modelled locally by relaxing the joint probability relation for independent variables $P(a,b)=P(a)P(b)$ outside classical settings, with complex/quaternion generators for the measurement outcomes…
The experimental violation of Bell inequality establishes necessary but not sufficient conditions that any theory must obey. Namely, a theory compatible with the experimental observations can satisfy at most two of the three hypotheses at…
For particles decaying without parity violation, it is impossible to reconstruct the full spin-density matrix from the velocities of their decay products. In this work, we consider Bell inequalities based on squares of spin operators. The…
Bell's theorem states that no description of a Bell experiment can be simultaneously local, realistic in the sense of counterfactual definiteness, and free of conspiracy between settings and hidden state. The recent generation of…
In their well-known argument against the completeness of quantum theory, Einstein, Podolsky, and Rosen (EPR) made use of a state that strictly correlates the positions and momenta of two particles. We prove the existence and uniqueness of…
The correlations in quantum networks have attracted strong interest with new types of violations of the locality. The standard Bell inequalities cannot characterize the multipartite correlations that are generated by multiple sources. The…
Wang et al. [Science Advances, 1 Aug 2025 Vol 11, Issue 31] recently reported an experiment that they interpret as demonstrating a violation of Bell's inequality using unentangled photons. Such a claim is highly controversial, since it is…
Recently, it was demonstrated by Son et al., Phys. Rev. Lett. \textbf{102}, 110404 (2009), that a separable bipartite continuous variable quantum system can violate the Clauser-Horne-Shimony-Holt (CHSH) inequality via operationally local…
In this paper we use the Lyndon-Shirshov basis to study the shuffle type polynomials. We give a free noncommutative binomial (or multinomial) theorem in terms of the Lyndon-Shirshov basis. Another noncommutative binomial theorem given by…