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arXiv · 2410.15790

Event-based quantum contextuality theory

Songyi Liu·Yongjun Wang·Baoshan Wang·Yunyi Jia
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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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Songyi Liu, Yongjun Wang, Baoshan Wang, Yunyi Jia. 2024-10-21. Event-based quantum contextuality theory. https://arxiv.org/abs/2410.15790

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