Violation of Bell's Inequalities in Jordan Triples and Jordan Algebras

Jan Hamhalter ; Ekaterina A. Turilova

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Noncommutative Analysis and Quantum Information Theory, Tome 324 (2024), pp. 225-237.

Résumé

We formulate and prove Bell's inequalities in the realm of JB$^*$ triples and JB$^*$ algebras. We show that the maximal violation of Bell's inequalities occurs in any JBW$^*$ triple containing a nonassociative $2$-Peirce subspace. Moreover, we show that the violation of Bell's inequalities in a nonmodular JBW$^*$ algebra and in an essentially nonmodular JBW$^*$ triple is generic. We describe the structure of maximal violators and its relation to the spin factor. In addition, we present a synthesis of available results based on a unified geometric approach.

Détail

Keywords: Bell's inequalities, JBW$^*$ algebra, JBW$^*$ triple.

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