Related papers: Bell's Inequalities and Algebraic Structure
We present a prescription for obtaining Bell's inequalities for N>2 observers involving more than two alternative measurement settings. We give examples of some families of such inequalities. The inequalities are violated by certain classes…
We study Bell's inequality in relation to the Einstein-Podolsky-Rosen paradox in the relativistic regime. For this purpose, a relativistically invariant observable is used in the calculation of the Bell's inequality, which results in the…
We review the status of Bell's inequalities in quantum information, stressing mainly the links with quantum key distribution and distillation of entanglement. We also prove that for all the eavesdropping attacks using one qubit, and for a…
Employing mutually-commuting von Neumann algebras to represent the algebra of observables on quantum systems provides a framework for studying quantum information theory in systems with infinite degrees of freedom and quantum field theory,…
We discuss the possibility of devising cosmological observables which violate Bell's inequalities. Such observables could be used to argue that cosmic scale features were produced by quantum mechanical effects in the very early universe. As…
In this paper, we will study some connections between Hilbert al- gebras and binary block-codes.With these codes, we can eassy obtain orders which determine suplimentary properties on these algebras. We will try to emphasize how, using…
It is not generally known, that the inequality that Bell derived using three random variables must be identically satisfied by any three corresponding data sets of plus and minus 1s that are writable on paper.This surprising fact is not…
We propose Bell inequalities for discrete or continuous quantum systems which test the compatibility of quantum physics with an interpretation in terms of deterministic hidden-variable theories. The wave function collapse that occurs in a…
Bell's inequality plays an important role with respect to the Einsteinian question about the physical reality of quantum theory. While Bell's inequality is usually viewed within the geometric framework of a Hilbert space quantum model, the…
Relations connecting violation of any Bell inequalities and the complementarity between visibility and distinguishability in the interferometric experiments with different sources of decoherence are presented. A boundary of local-realistic…
The author has recently introduced abstract algebraic frameworks of analogical proportions and similarity within the general setting of universal algebra. The purpose of this paper is to build a bridge from similarity to analogical…
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…
Errors in Eberly's derivation of several Bell inequalities are pointed out: (1) it is based on an equation that is incorrect; (2) it uses neither two-particle states nor locality to derive Bell's inequalities and; (3) it does not use…
Multi-qudit systems are studied in tomographic probability representations of quantum qudit states. Results of calculations for Bell-type numbers within the framework of classical probability theory and in quantum tomography are compared.…
In this pages I give an overview of the relationship between Model Theory, Arithmetic and Algebraic Geometry. The topics will be the basic ones in the area, so this is just an invitation, in the presentation of topics I mainly follow the…
The notion of semi-BCI algebras is introduced and some of its properties are investigated. This algebra is another generalization for BCI-algebras. It arises from the "intervalization" of BCI algebras. Semi-BCI have a similar structure to…
We derive both numerically and analytically Bell inequalities and quantum measurements that present enhanced resistance to detector inefficiency. In particular we describe several Bell inequalities which appear to be optimal with respect to…
Bell inequalities reveal the fundamentally nonlocal character of quantum mechanics. In this regard, one of the interesting problems is to explore all possible Bell inequalities that demonstrate a gap between local and nonlocal quantum…
The assumptions required for the derivation of Bell inequalities are not usually satisfied for random fields in which there are any thermal or quantum fluctuations, in contrast to the general satisfaction of the assumptions for classical…
The notion of equivalence of maximally entangled bases of bipartite d-dimensional Hilbert spaces is introduced. An explicit method of inequivalent bases construction is presented.