Event-based contextuality theory

• URL: http://arxiv.org/abs/2410.15790v1
• Date: Mon, 21 Oct 2024 08:55:43 GMT
• Title: Event-based contextuality theory
• Authors: Songyi Liu, Yongjun Wang, Baoshan Wang,
• Abstract summary: This paper analyses the challenges faced by some known contextuality theories, and establishes an event-based contextuality theory with partial Boolean algebra to overcome them. The theory can handle the scenarios composed of general projectors and observables, and provides a unified mathematical structure to investigate the hierarchy of quantum contextuality.
• Score: 1.9266988189076035
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 analyses the challenges faced by some known contextuality theories, and establishes an event-based contextuality theory with partial Boolean algebra to overcome them. The theory can handle the scenarios composed of general projectors and observables, and provides a unified mathematical structure to investigate the hierarchy of quantum contextuality. It also introduces a tool to extend some known results from rank-1 cases to general cases. For example, we get a Kochen-Specker set with 12 projectors from the Cabello-Estebaranz-Garcia set with 18 vectors.

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