Geodesic
Violation of Bell's Inequalities in Jordan Triples and Jordan Algebras
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Noncommutative Analysis and Quantum Information Theory, Tome 324 (2024), pp. 225-237

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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.
Keywords: Bell's inequalities, JBW$^*$ algebra, JBW$^*$ triple. 
@article{TM_2024_324_a18,
     author = {Jan Hamhalter and Ekaterina A. Turilova},
     title = {Violation of {Bell's} {Inequalities} in {Jordan} {Triples} and {Jordan} {Algebras}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {225--237},
     publisher = {mathdoc},
     volume = {324},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2024_324_a18/}
}
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Jan Hamhalter; Ekaterina A. Turilova. Violation of Bell's Inequalities in Jordan Triples and Jordan Algebras. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Noncommutative Analysis and Quantum Information Theory, Tome 324 (2024), pp. 225-237. http://geodesic.mathdoc.fr/item/TM_2024_324_a18/