Twelve-dimensional Pauli group contextuality

TL;DR

This paper investigates quantum contextuality in twelve-dimensional qudit systems, demonstrating that such contextuality emerges at this dimension through specific configurations and graph-theoretic characterizations.

Contribution

It identifies the emergence of quantum contextuality at dimension twelve in qudit systems and employs Shannon capacity to analyze the orthogonality graphs involved.

Findings

Quantum contextuality appears at dimension twelve.

Orthogonality graphs are characterized using Shannon capacity.

Arithmetical properties underpin qudit contextuality.

Abstract

The goal of the paper is to check whether the real eigenstates of the observables in the single qudit Pauli group may lead to quantum contextuality, the property that mutually compatible and independent experiments depend on each other. We find that quantum contextuality crops up at dimension twelve in various configurations with a few rays. We use the Shannon capacity for characterizing the corresponding orthogonality graphs. Some arithmetical properties underlying the qudit contextuality are outlined.