Related papers: Groups, Platonic solids and Bell inequalities

Bell-inequality violations reveal the presence of quantum correlations between two particles that have interacted and then separated. Their generalisation to quantum fields is necessary to study a number of field-theoretic setups, such as…

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…

First, we present a Bell type inequality for n qubits, assuming that m out of the n qubits are independent. Quantum mechanics violates this inequality by a ratio that increases exponentially with m. Hence an experiment on n qubits violating…

A braided generalization of the concept of Hopf algebra (quantum group) is presented. The generalization overcomes an inherent geometrical inhomogeneity of quantum groups, in the sense of allowing completely pointless objects. All…

In the present article, based on the formalism introduced in [Loubenets, J. Math. Phys. 53, 022201 (2012)], we derive for a pure bipartite quantum state a new upper bound on its maximal violation of general Bell inequalities. This new bound…

Bell's theorem is typically understood as the proof that quantum theory is incompatible with local-hidden-variable models. More generally, we can see the violation of a Bell inequality as witnessing the impossibility of explaining quantum…

Within the frame of a Group Approach to Quantization anomalies arise in a quite natural way. We present in this talk an analysis of the basic obstructions that can be found when we try to translate symmetries of the Newton equations to the…

Leggett formulated an inequality which seems to generalize the Bell theorem to non-local hidden variable theories. Leggett inequality is violated by quantum mechanics, as was confirmed by experiment. However, a careful analysis reveals that…

We consider the action of a parabolic subgroup of the General Linear Group on a metabelian ideal. For those actions, we classify actions with finitely many orbits using methods from representation theory.

The paper discusses the concept of separation of quantum mechanical systems in the algebraic approach. We review known theorems, then establish a link between the C*-algebraic and the corresponding W*-algebraic concepts. A characterization…

The question of how large Bell inequality violations can be, for quantum distributions, has been the object of much work in the past several years. We say that a Bell inequality is normalized if its absolute value does not exceed 1 for any…

In this note some properties of the sum of element orders of a finite abelian group are studied.

The algebraic derivation of the numerical limits of Bell inequalities in either three or four random variables is independent of the assumption of randomness.The limits of the inequalities follow as mathematical consequences of their…

Full-correlation Bell-like inequalities represent an important subclass of Bell-like inequalities that have found applications in both a better understanding of fundamental physics and in quantum information science. Loosely speaking, these…

We prove that the locality condition is irrelevant to Bell in equality. We check that the real origin of the Bell's inequality is the assumption of applicability of classical (Kolmogorovian) probability theory to quantum mechanics. We…

Characterizing the set of all Bell inequalities is a notably hard task. An insightful method of solving it in case of Bell correlation inequalities for scenarios with two dichotomic measurements per site - for arbitrary number of parties -…

It was recently argued that quantum field theories possess one-form and higher-form symmetries, labelled `generalized global symmetries.' In this paper, we describe how those higher-form symmetries can be understood mathematically as…

We study the relation between the quantum games, communication complexity problems and Bell inequalities. In particular we are interested in answering the question whether for every element of one of these groups there is a corresponding…

The statistics behind Bell's inequality is demonstrated to allow a Kolmogorovian (i.e. classical) model of probabilities that recovers the quantum covariance.

We study the relation between violation of Bell inequalities and distillability properties of quantum states. Recently, D\"ur has shown that there are some multiparticle bound entangled states, non-separable and non-distillable, that…