# Classifying space for quantum contextuality

## TL;DR

This paper introduces a topological space framework to analyze quantum contextuality, linking algebraic topology invariants to physical quantities and interpreting the Wigner function as a K-theory class.

## Contribution

It constructs a classifying space for quantum contextuality and connects cohomological invariants and the Wigner function to topological and K-theoretic concepts.

## Key findings

- Cohomological invariants correspond to physical contextuality measures
- Wigner function interpreted as a twisted K-theory class
- Provides a new topological perspective on quantum contextuality

## Abstract

We construct a topological space to study contextuality in quantum mechanics. The resulting space is a classifying space in the sense of algebraic topology. Cohomological invariants of our space correspond to physical quantities relevant to the study of contextuality. Within this framework the Wigner function of a quantum state can be interpreted as a class in the twisted $K$-theory of the classifying space.