Related papers: Separation theorems and Bell inequalities in algeb…
I review the various algebraic foundations of quantum mechanics. They have been suggested since the birth of this theory till up to last year. They are the following ones: Heisenberg-Born-Jordan (1925), Weyl (1928), Dirac (1930), von…
An abstract treatment of Bell inequalities is proposed, in which the parameters characterizing Bell's observable can be times rather than directions. The violation of a Bell inequality might then be taken to mean that a property of a system…
Since John Bell formulated his paramount inequality for a pair of spin-$1/2$ particles, quantum mechanics has been confronted with the postulates of local realism with various equivalent configurations. Current technology, with its advanced…
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…
We examine the use of noiseless subsystems for quantum information processing between two parties who do not share a common reference frame. In particular we focus on Bell inequalities in curved spaces and outline a theoretical procedure to…
Within the framework of the algebraic approach the problem of hidden parameters in quantum mechanics is surveyed. It is shown that the algebraic formulation of quantum mechanics permits introduction of a specific hidden parameter, which has…
Decompositional theories describe the ways in which a global physical system can be split into subsystems, facilitating the study of how different possible partitions of a same system interplay, e.g. in terms of inclusions or signalling. In…
We review our approach to quantum mechanics adding also some new interesting results. We start by giving proof of two important theorems on the existence of the and Clifford algebras. This last algebra gives proof of the von Neumann basic…
A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating…
A simple minimalist argument is given for why some correlations between quantum systems boggle our classical intuition. The argument relies on two elementary physical assumptions, and recovers the standard experimentally-testable Bell…
A recent experiment yielding results in agreement with quantum theory and violating Bell inequalities was interpreted [Nature 526 (29 Octobert 2015) p. 682 and p. 649] as ruling out any local realistic theory of nature. But quantum theory…
The derivation of macroscopic irreversible dynamics of nonequilibrium systems from microscopic equations was recently revisited from the point of view of infinitely extended quantum systems. Here we have briefly reviewed the $C^*$ algebra…
Between 1964 and 1990, the notion of nonlocality in Bell's papers underwent a profound change as his nonlocality theorem gradually became detached from quantum mechanics, and referred to wider probabilistic theories involving correlations…
This survey article is concerned with the modeling of the kinematical structure of quantum systems in an algebraic framework which eliminates certain conceptual and computational difficulties of the conventional approaches. Relying on the…
An algebraic approach to the study of quantum mechanics on configuration spaces with a finite fundamental group is presented. It uses, in an essential way, the Gelfand-Naimark and Serre-Swan equivalences and thus allows one to represent…
In contrast to the spatial Bell's inequalities, which probe entanglement between spatially-separated systems, the Leggett-Garg inequalities test the correlations of a single system measured at different times. Violation of a genuine…
The statement of E.R. Loubenets, Phys. Rev. A 69, 042102 (2004), that separable states can violate classical probabilistic constraints is based on a misleading definition of classicality, which is much narrower than Bell's concept of local…
We derive ``Bell inequalities'' in four dimensional phase space and prove the following ``three marginal theorem'' for phase space densities $\rho(\overrightarrow{q},\overrightarrow{p})$, thus settling a long standing conjecture : ``there…
We present a set of Bell inequalities which are sufficient and necessary for separability of general pure multipartite quantum states in arbitrary dimensions. The relations between Bell inequalities and distillability are also studied. We…
The standard C*-algebraic version of the algebra of canonical commutation relations, the Weyl algebra, frequently causes difficulties in applications since it neither admits the formulation of physically interesting dynamical laws nor does…