Homotopical approach to quantum contextuality

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.

20 pages, 8 figures

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• Six-dimensional light-front Wigner distribution of hadrons
• Wigner and friends, a map is not the territory! Contextuality in multi-agent paradoxes
• No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords
• An abstract structure determines the contextuality degree of observable-based Kochen-Specker proofs
• Commutative d-Torsion K-Theory and Its Applications
• Differential Geometry of Contextuality
• Analogs of absolutely maximally entangled states in nonlocal correlations via the sheaf-theoretic framework and its applications