# Homotopical approach to quantum contextuality

## TL;DR

This paper explores how the commutativity structure of quantum observables influences the possibility of parity-based contextuality proofs, using topological methods to generalize previous results.

## Contribution

It introduces a topological criterion that determines when the commutativity structure alone suffices for quantum contextuality proofs, extending Arkhipov's earlier work.

## Key findings

- Established a topological criterion for contextuality proofs
- Generalized Arkhipov's earlier results
- Connected commutativity structure with contextuality viability

## Abstract

We consider the phenomenon of quantum mechanical contextuality, and specifically parity-based proofs thereof. Mermin's square and star are representative examples. Part of the information invoked in such contextuality proofs is the commutativity structure among the pertaining observables. We investigate to which extent this commutativity structure alone determines the viability of a parity-based contextuality proof. We establish a topological criterion for this, generalizing an earlier result by Arkhipov.