Almost Equivalent Paradigms of Contextuality

TL;DR

This paper demonstrates the equivalence of two major frameworks for understanding contextuality in physics, providing a unified approach and a new method for detecting contextuality in scenarios with preparations and measurements.

Contribution

It establishes a categorical isomorphism between the sheaf-theoretic and equivalence-based frameworks, unifying their perspectives on contextuality.

Findings

Frameworks are equivalent under certain conditions

A categorical isomorphism is established

A canonical method for detecting contextuality is derived

Abstract

Various frameworks that generalise the notion of contextuality in theories of physics have been proposed; one is the sheaf-theoretic approach by Abramsky and Brandenburger; an other is the equivalence-based approach by Spekkens. We show that these frameworks are equivalent for scenarios with preparations and measurements, whenever factorizability is justified. This connection gives rise to a categorical isomorphism between suitable categories. We combine the advantages of the two approaches to derive a canonical method for detecting contextuality in such settings.