Atom graph, partial Boolean algebra and quantum contextuality

• URL: http://arxiv.org/abs/2409.17651v1
• Date: Thu, 26 Sep 2024 08:57:04 GMT
• Title: Atom graph, partial Boolean algebra and quantum contextuality
• Authors: Songyi Liu, Yongjun Wang, Baoshan Wang, Jian Yan, Heng Zhou,
• Abstract summary: We show that quantum systems are uniquely determined by their atom graphs. We also present a general and parametric description for Kochen-Specker theorem based on graphs.
• Score: 3.9474648943255937
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Partial Boolean algebra underlies the quantum logic as an important tool for quantum contextuality. We propose the notion \textit{atom graphs} to reveal the graph structure of partial Boolean algebra for quantum systems by proving that (i) the partial Boolean algebras for quantum systems are determined by their atom graphs; (ii) the states on atom graphs can be extended uniquely to the partial Boolean algebras, and (iii) each exclusivity graph is an induced graph of an atom graph. (i) and (ii) show that the quantum systems are uniquely determined by their atom graphs. which proves the reasonability of graphs as the models of quantum experiments. (iii) establishes a connection between partial Boolean algebra and exclusivity graphs, and introduces a method to express the exclusivity experiments more precisely. We also present a general and parametric description for Kochen-Specker theorem based on graphs, which gives a type of non-contextuality inequality for KS contextuality.

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