Related papers: The extension problem for partial Boolean structur…
Violations of Bell inequalities in classical optics have been demonstrated in terms of field mean intensities and correlations, however, the quantum meaning of violations point to statistics and probabilities. We present a violation of Bell…
The problem of construction of irreducible representations of quantum $A^q_n$ algebras is solved at the level of explicit integration of the linear (inhomogeneous) system in finite differences in the n-dimensional space. The general…
I review the relation of the Bell inequalities - characteristic of (classical) probabilities defined on Boolean logics - with noncontextual and local hidden variables theories of quantum mechanics and with quantum information.
Bell inequalities are mathematical constructs that demarcate the boundary between quantum and classical physics. A new class of multiplicative Bell inequalities originating from a volume maximization game (based on products of correlators…
We present generic Bell inequalities for multipartite multi-dimensional systems. The inequalities that any local realistic theories must obey are violated by quantum mechanics for even-dimensional multipartite systems. A large set of…
Quantum mechanics led to spectacular technological developments, discovery of new constituents of matter and new materials. However there is still no consensus on its interpretation and limitations. Some scientists and scientific writers…
The discovery of Bell that there exist quantum correlations that cannot be reproduced classically is one of the most important in the foundations of quantum mechanics, as well as having practical implications. Bell's result was originally…
Two notions of nonclassicality that have been investigated intensively are: (i) negativity, that is, the need to posit negative values when representing quantum states by quasiprobability distributions such as the Wigner representation, and…
An information-theoretic temporal Bell inequality is formulated to contrast classical and quantum computations. Any classical algorithm satisfies the inequality, while quantum ones can violate it. Therefore, the violation of the inequality…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
This article surveys key conceptual and interpretational developments in quantum mechanics, tracing the theory from its foundational postulates to contemporary discussions of measurement, nonlocality, and the emergence of classicality.…
In this article, the weakest possible theorem providing a foundation for the Hilbert space formalism of quantum theory is stated. The necessary postulates are formulated, and the mathematics is spelt out in detail. It is argued that, from…
This paper illustrates the relationship between boolean propositional algebra and semirings, presenting some results of partial ordering on boolean propositional algebras, and the necessary conditions to represent a boolean propositional…
We study the physical content of the PT-symmetric complex extension of quantum mechanics as proposed in Bender et al, Phys. Rev. Lett. 80, 5243 (1998) and 89, 270401 (2002), and show that as a fundamental probabilistic physical theory it is…
We obtain a general connection between a quantum advantage in communication complexity and non-locality. We show that given any protocol offering a (sufficiently large) quantum advantage in communication complexity, there exists a way of…
In this article we consider partial abelianization of associative algebra with respect to a subalgebra. This notion is a generalization of usual abelianization of associative algebra and has an application in Quantum Mechanics and Quantum…
It is a recent realization that many of the concepts and tools of causal discovery in machine learning are highly relevant to problems in quantum information, in particular quantum nonlocality. The crucial ingredient in the connection…
The so-called classical limit of quantum mechanics is generally studied in terms of the decoherence of the state operator that characterizes a system. This is not the only possible approach to decoherence. In previous works we have…
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…
In Part I of this series we presented the general ideas of applying group-algebraic methods for describing quantum systems. The treatment was there very "ascetic" in that only the structure of a locally compact topological group was used.…