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Auteurs principaux:	Liu, Songyi, Wang, Yongjun, Wang, Baoshan, Yan, Jian, Zhou, Heng
Format:	Preprint
Publié:	2024
Sujets:	Quantum Physics Logic
Accès en ligne:	https://arxiv.org/abs/2411.18146
Tags:	Ajouter un tag Pas de tags, Soyez le premier à ajouter un tag!

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author	Liu, Songyi Wang, Yongjun Wang, Baoshan Yan, Jian Zhou, Heng
author_facet	Liu, Songyi Wang, Yongjun Wang, Baoshan Yan, Jian Zhou, Heng
contents	The quantum mechanics is proved to admit no hidden-variable in 1960s, which means the quantum systems are contextual. Revealing the mathematical structure of quantum mechanics is a significant task. We develop the approach of partial Boolean algebra to characterize the contextuality theory with local consistency and exclusivity, and then prove that the finite dimensional quantum systems are determined by atoms using two graph structure theorems. We also generalize our work to infinite dimensional cases. Our conclusions indicate that the quantum mechanics is a graph-structured combination of multiple hidden-variable theories, and provide a precise mathematical framework for quantum contextuality.
format	Preprint
id	arxiv_https___arxiv_org_abs_2411_18146
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Graph structure of quantum mechanics Liu, Songyi Wang, Yongjun Wang, Baoshan Yan, Jian Zhou, Heng Quantum Physics Logic The quantum mechanics is proved to admit no hidden-variable in 1960s, which means the quantum systems are contextual. Revealing the mathematical structure of quantum mechanics is a significant task. We develop the approach of partial Boolean algebra to characterize the contextuality theory with local consistency and exclusivity, and then prove that the finite dimensional quantum systems are determined by atoms using two graph structure theorems. We also generalize our work to infinite dimensional cases. Our conclusions indicate that the quantum mechanics is a graph-structured combination of multiple hidden-variable theories, and provide a precise mathematical framework for quantum contextuality.
title	Graph structure of quantum mechanics
topic	Quantum Physics Logic
url	https://arxiv.org/abs/2411.18146

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