Classifying space for 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.

30 pages, 1 figure

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• Hidden Variables and the Two Theorems of John Bell
• Computational power of correlations
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Cited by in corpus (2)

• Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements
• Commutative d-Torsion K-Theory and Its Applications