Related papers: Bell's Inequalities and Algebraic Structure
Contrary to what Lambare [arXiv:2008.00369] assumes, in non-Newtonian calculus (a calculus based on non-Diophantine arithmetic) an integral is typically given by a nonlinear map. This is the technical reason why all the standard proofs of…
We attempt to survey recent results and open problems connected to Lieb-Thirring inequalities.
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…
We give an expression for a generalized numerical radius of Hilbert space operators and then apply it to obtain upper and lower bounds for the generalized numerical radius. We also establish some generalized numerical radius inequalities…
A set of Bell inequalities classifying the quantum entanglement of four-qubit states is presented. These inequalities involve only two measurement settings per observer and can characterize fully separable, bi-separable and tri-separable…
Bell's inequalities, in the form given by Cerf and Adami, are derived from the combination of the second law of thermodynamics and the Markov postulate. Violations of these inequalities are discussed in terms of the mixing characteristics…
There is a lot of information available concerning Hardy-Hilbert type inequalities in one or more dimensions. In this paper we introduce the development of such inequalities on homogeneous groups. Moreover, we point out a unification of…
New results related to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.
Solid experimental evidence has now been obtained that confirms the violation of Bell's inequality in tests of maximally entangled qubit pairs. This violation is widely interpreted as definitive proof of the impossibility of describing…
A mixture of an historical article, and of a survey of recent developments, containing also a couple of new results.
The Bell inequality constrains the outcomes of measurements on pairs of distant entangled particles. The Bell contradiction states that the Bell inequality is inconsistent with the calculated outcomes of these quantum experiments. This…
Quantum correlations which violate a Bell inequality are presumed to power better-than-classical protocols for solving communication complexity problems (CCPs). How general is this statement? We show that violations of correlation-type Bell…
In the first part of this thesis Bell's theorem is revisited. It points at a difference between the quantum and the classical world. This difference is often behind the advantages of solutions using quantum mechanics. New and more general…
Leibniz algebras are certain generalization of Lie algebras. In this paper we survey the important results in Leibniz algebras which are analogs of corresponding results in Lie algebras. In particular we highlight the differences between…
Various Bell inequalities are trivial algebraic properties satisfied by each line of particular data spreadsheets.It is surprising that their violation in some experiments, allows to speculate about the existence of nonlocal influences in…
Many Bell test results violate Bell's inequality. The premise of Bell's inequality is local determinism. We propose that, it can't be proved that something's mechanism isn't deterministic; if loopholes are not the reason of violation of…
We analyze the structure of correlations among more than two quantum systems. We introduce a classification of correlations based on the concept of non-separability, which is different {\em a priori} from the concept of entanglement.…
We give a simple proof of Bell's inequality in quantum mechanics which, in conjunction with experiments, demonstrates that the local hidden variables assumption is false. The proof sheds light on relationships between the notion of causal…
We survey several significant results on the Bohr inequality and presented its generalizations in some new approaches. These are some Bohr type inequalities of Hilbert space operators related to the matrix order and the Jensen inequality.…
A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.