The logical structure of contextuality and nonclassicality

TL;DR

This paper introduces a logical framework using exclusive partial Boolean algebras to unify the description of contextuality and nonclassicality in quantum systems, providing minimal configurations for various quantum phenomena.

Contribution

It presents a novel logical and mathematical framework that unifies and characterizes quantum contextuality and nonclassicality across different systems, with minimal configurations.

Findings

12 projectors suffice for Kochen-Specker scenarios

10 projectors suffice for state-independent contextuality

3 observables suffice to witness quantum contextuality

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.