The logical structure of contextuality and nonclassicality
Abstract
Quantum contextuality represents a fundamental form of nonclassicality in quantum mechanics. To provide a more complete characterization of nonclassical properties in quantum systems, we adopt a logical perspective and propose a mathematical framework based on exclusive partial Boolean algebras (epBAs). This framework enables a unified description of contextuality and nonclassicality across finite general, quantum, and classical systems. We establish a unified and minimal classical counterpart for any finite general system. Within this framework, we formalize major categories of quantum contextuality, demonstrating that: 12 projectors suffice to generate Kochen-Specker scenarios; 10 projectors suffice to witness state-independent contextuality; and 3 observables suffice to witness quantum contextuality. Finally, we prove that contextuality is a sufficient but not necessary condition for nonclassicality.
Cite
@article{arxiv.2506.15071,
title = {The logical structure of contextuality and nonclassicality},
author = {Songyi Liu and Yongjun Wang and Baoshan Wang and Chang He and Jincheng Wang},
journal= {arXiv preprint arXiv:2506.15071},
year = {2025}
}