Logic of Local Inference for Contextuality in Quantum Physics and Beyond

TL;DR

This paper develops a new logical framework based on topology and category theory to analyze local consistency in quantum contextuality, extending previous approaches that focused on global inconsistency.

Contribution

It introduces a logic of local inference using context-sensitive theories and models in regular categories, capturing the local consistency aspect of contextuality.

Findings

Provides a uniform framework for local consistency analysis

Lays foundation for using contextuality as a computational resource

Extends topological and categorical methods to quantum contextuality

Abstract

Contextuality in quantum physics provides a key resource for quantum information and computation. The topological approach in [Abramsky and Brandenburger, New J. Phys., 2011, Abramsky et al., CSL 2015, 2015] characterizes contextuality as "global inconsistency" coupled with "local consistency", revealing it to be a phenomenon also found in many other fields. This has yielded a logical method of detecting and proving the "global inconsistency" part of contextuality. Our goal is to capture the other, "local consistency" part, which requires a novel approach to logic that is sensitive to the topology of contexts. To achieve this, we formulate a logic of local inference by using context-sensitive theories and models in regular categories. This provides a uniform framework for local consistency, and lays a foundation for high-level methods of detecting, proving, and moreover using contextuality as computational resource.