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

IF 0.4 4区数学 Q4 MATHEMATICS

Proceedings of the Steklov Institute of Mathematics Pub Date : 2024-07-11 DOI:10.1134/s008154382401019x

Jan Hamhalter, Ekaterina A. Turilova

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.

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乔丹三元组和乔丹代数中贝尔不等式的违反

Abstract 我们在JB（^*\）三元组和JB（^*\）代数的领域中提出并证明了贝尔不等式。我们证明了贝尔不等式的最大违反发生在任何包含一个非关联 \(2\)-Peirce 子空间的 JBW\(^*\) 三元组中。此外，我们还证明了在非模态 JBW\(^*\) 代数和本质上非模态的 JBW\(^*\) 三重中对贝尔不等式的违反是通用的。我们描述了最大违反者的结构及其与自旋因子的关系。此外，我们还介绍了基于统一几何方法的现有结果的综合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the Steklov Institute of Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

20.00%

发文量

审稿时长

4-8 weeks

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.