Graph-theoretic strengths of contextuality

TL;DR

This paper compares two mathematical frameworks for Bell and contextuality inequalities, introduces graph-theoretic methods for proofs and state identification, and applies these to stabilizer quantum mechanics to explore contextuality as a computational resource.

Contribution

It unifies two approaches to nonlocality and contextuality using graph theory and demonstrates their application to quantum computation scenarios.

Findings

Graph-theoretic methods simplify proofs of nonlocality and contextuality.

Identifies states with strong nonlocality and contextuality in stabilizer quantum mechanics.

Provides a unified framework linking different inequality approaches.

Abstract

Cabello-Severini-Winter and Abramsky-Hardy (building on the framework of Abramsky-Brandenburger) both provide classes of Bell and contextuality inequalities for very general experimental scenarios using vastly different mathematical techniques. We review both approaches, carefully detail the links between them, and give simple, graph-theoretic methods for finding inequality-free proofs of nonlocality and contextuality and for finding states exhibiting strong nonlocality and/or contextuality. Finally, we apply these methods to concrete examples in stabilizer quantum mechanics relevant to understanding contextuality as a resource in quantum computation.