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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2024, Volume 324, Pages 225–237
DOI: https://doi.org/10.4213/tm4367 (Mi tm4367) 		 
Violation of Bell's Inequalities in Jordan Triples and Jordan Algebras

Jan Hamhaltera, Ekaterina A. Turilovab

a Czech Technical University in Prague, Faculty of Electrical Engineering, Technická 2, 166 27 Prague 6, Czech Republic
b Kazan Federal University, Kremlevskaya ul. 18, Kazan, 420008 Russia
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DOI: https://doi.org/10.4213/tm4367
Abstract: 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.
Funding agency Grant number
Center of Advanced Applied Sciences CZ.02.1.01/0.0/0.0/16_019/0000778
Czech Science Foundation (GACR) GA23-04776
The work of J. Hamhalter was supported by the Centre of Advanced Applied Sciences (project OPVVV CAAS CZ.02.1.01/0.0/0.0/16_019/0000778) and by the Czech Science Foundation (grant GA23-04776S, “Interplay of algebraic, metric, geometric and topological structures on Banach spaces”).
Received: June 15, 2023
Revised: July 19, 2023
Accepted: August 18, 2023
English version:
Proceedings of the Steklov Institute of Mathematics, 2024, Volume 324, Pages 213–224
DOI: https://doi.org/10.1134/S008154382401019X
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: Jan Hamhalter, Ekaterina A. Turilova, “Violation of Bell's Inequalities in Jordan Triples and Jordan Algebras”, Noncommutative Analysis and Quantum Information Theory, Collected papers. Dedicated to Academician Alexander Semenovich Holevo on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 324, Steklov Math. Inst., Moscow, 2024, 225–237; Proc. Steklov Inst. Math., 324 (2024), 213–224
Citation in format AMSBIB
\Bibitem{HamTur24}
\by Jan~Hamhalter, Ekaterina~A.~Turilova
\paper Violation of Bell's Inequalities in Jordan Triples and Jordan Algebras
\inbook Noncommutative Analysis and Quantum Information Theory
\bookinfo Collected papers. Dedicated to Academician Alexander Semenovich Holevo on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 324
\pages 225--237
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4367}
\crossref{https://doi.org/10.4213/tm4367}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4767960}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 324
\pages 213--224
\crossref{https://doi.org/10.1134/S008154382401019X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85198142160}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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