Event-based quantum contextuality theory

TL;DR

This paper develops an event-based mathematical framework for quantum contextuality that extends previous theories to general projectors, establishing a hierarchy and clarifying the strength of Kochen-Specker contextuality.

Contribution

It introduces an event-based contextuality theory using exclusive partial Boolean algebra, applicable to general projectors, and establishes a hierarchy of contextuality.

Findings

Kochen-Specker contextuality is equivalent to state-independent strong contextuality.

Kochen-Specker contextuality is the strongest form when considering strength and proportion.

The theory handles scenarios with general projectors, unlike previous models.

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.