{"title":"Violation of Bell’s Inequalities in Jordan Triples and Jordan Algebras","authors":"Jan Hamhalter, Ekaterina A. Turilova","doi":"10.1134/s008154382401019x","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We formulate and prove Bell’s inequalities in the realm of JB<span>\\(^*\\)</span> triples and JB<span>\\(^*\\)</span> algebras. We show that the maximal violation of Bell’s inequalities occurs in any JBW<span>\\(^*\\)</span> triple containing a nonassociative <span>\\(2\\)</span>-Peirce subspace. Moreover, we show that the violation of Bell’s inequalities in a nonmodular JBW<span>\\(^*\\)</span> algebra and in an essentially nonmodular JBW<span>\\(^*\\)</span> 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. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"42 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Steklov Institute of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s008154382401019x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
Proceedings of the Steklov Institute of Mathematics is a cover-to-cover translation of the Trudy Matematicheskogo Instituta imeni V.A. Steklova of the Russian Academy of Sciences. Each issue ordinarily contains either one book-length article or a collection of articles pertaining to the same topic.
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