Event-based quantum contextuality theory

• URL: http://arxiv.org/abs/2410.15790v3
• Date: Thu, 16 Jan 2025 07:42:08 GMT
• Title: Event-based quantum contextuality theory
• Authors: Songyi Liu, Yongjun Wang, Baoshan Wang, Yunyi Jia,
• Abstract summary: This paper overcomes the challenges faced by some known contextuality theories by establishing an event-based contextuality theory. Our theory provides a precise mathematical framework for quantum contextuality, which can handle the scenarios composed of general projectors. We conclude that the Kochen-Specker contextuality is equivalent to the state-independent strong contextuality for finite dimensional quantum systems.
• Score: 9.808029647992774
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• Abstract: Fully revealing the mathmatical structure of quantum contextuality is a significant task, while some known contextuality theories are only applicable for rank-1 projectors. That is because they adopt the observable-based definitions. This paper overcomes the challenges faced by some known contextuality theories by establishing an event-based contextuality theory with exclusive partial Boolean algebra, which is used to describe the contextual systems with local consistency and exclusivity principle. Our theory provides a precise mathematical framework for quantum contextuality, which can handle the scenarios composed of general projectors, and introduces a more complete contextuality hierarchy. We conclude that the Kochen-Specker contextuality is equivalent to the state-independent strong contextuality for finite dimensional quantum systems. Therefore, when considering both the strength and proportion of contextual quantum states, Kochen-Specker contextuality is the strongest.

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