Event-based quantum contextuality theory
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.
Cite
@article{arxiv.2410.15790,
title = {Event-based quantum contextuality theory},
author = {Songyi Liu and Yongjun Wang and Baoshan Wang and Yunyi Jia},
journal= {arXiv preprint arXiv:2410.15790},
year = {2025}
}