Related papers: Groups, Platonic solids and Bell inequalities
The Bell's basis is composed of four maximally entangled states of two qubits, named Bell states. They are usual tools in many theoretical studies and experiments. The aim of this paper is to find out the symmetries that determine a Bell…
Let A be an abelian surface over F_q, the field of q elements. The rational points on A/\F_q form an abelian group A(\F_q) \simeq \Z/n_1\Z \times \Z/n_1 n_2 \Z \times \Z/n_1 n_2 n_3\Z \times\Z/n_1 n_2 n_3 n_4\Z. We are interested in knowing…
The action of the idempotent deformations on finite groups is discussed. This action is described in terms of the homological properties of groups. The orbits of finite simple groups are determined.
Bell's theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of pre-existing local properties. We give an…
We derive tight Bell's inequalities for N>2 observers involving more than two alternative measurement settings. We give a necessary and sufficient condition for a general quantum state to violate the new inequalities. The inequalities are…
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…
In a quantum network, distant observers sharing physical resources emitted by independent sources can establish strong correlations, which defy any classical explanation in terms of local variables. We discuss the characterization of…
What is the communication cost of simulating the correlations produced by quantum theory? We generalize Bell inequalities to the setting of local realistic theories augmented by a fixed amount of classical communication. Suppose two parties…
In this paper, we introduce a new function related to the sum of element orders of finite groups. It is used to give some criteria for a finite group to be cyclic, abelian, nilpotent, supersolvable and solvable, respectively.
We give a multidimensional generalisation of the complete set of Bell-correlation inequalities given by Werner and Wolf, and by Zukowski and Brukner, for the two-dimensional case. Our construction applies for the n parties, two-observables…
We numerically investigate entropic Bell inequalities for a pair of entangled qutrits using information-theoretic distances. We show that for this class of inequalities Tsallis entropy is more suitable than Shannon as it reveals…
This article discusses the main aspects related to Bell's inequality, both theoretical and experimental. A new derivation of Bell's inequality is also presented, which stands out for its mathematical simplicity. The exposition is mainly…
A survey of problems, conjectures, and theorems about quasi-isometric classification and rigidity for finitely generated solvable groups.
Bell-inequality checks constitute a probe of entanglement -- given a source of entangled particles, their violation are a signature of the non-local nature of quantum mechanics. Here, we study a solid state device producing pairs of…
We discuss a class of proofs of Bell-type inequalities that are based on tables of potential outcomes. These proofs state in essence: if one can only imagine (or write down in a table) the potential outcome of a hidden parameter model for…
The correspondence principle suggests that quantum systems grow classical when large. Classical systems cannot violate Bell inequalities. Yet agents given substantial control can violate Bell inequalities proven for large-scale systems. We…
We establish discrete Korn type inequalities for particle systems within the general class of objective structures that represents a far reaching generalization of crystal lattice structures. For space filling configurations whose symmetry…
We introduce a hierarchy of conditions necessarily satisfied by any distribution P(ab) representing the probabilities for two separate observers to obtain outcomes a and b when making local measurements on a shared quantum state. Each…
We analyse the recent claim that a violation of a Bell's inequality has been observed in the $B$--meson system [A. Go, {\em Journal of Modern Optics} {\bf 51} (2004) 991]. The results of this experiment are a convincing proof of quantum…
The characterization of the set of quantum correlations is a problem of fundamental importance in quantum information. The question whether every proper (tight) Bell inequality is violated in Quantum theory is an intriguing one in this…