Homotopical approach to quantum contextuality

Cihan Okay and Robert Raussendorf

Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada
Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC, Canada

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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.

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[1] Yingda Han, Tianbo Liu, and Bo-Qiang Ma, "Six-dimensional light-front Wigner distribution of hadrons", Physics Letters B 830, 137127 (2022).

[2] Shane Mansfield, "Contextuality is topological", Quantum Views 4, 31 (2020).

[3] Cihan Okay, "Commutative d-torsion K-theory and its applications", Journal of Mathematical Physics 62 10, 102201 (2021).

[4] Philippe Grangier, "Contextual Inferences, Nonlocality, and the Incompleteness of Quantum Mechanics", Entropy 23 12, 1660 (2021).

[5] Hammam Qassim and Joel J. Wallman, "Classical vs quantum satisfiability in linear constraint systems modulo an integer", Journal of Physics A Mathematical General 53 38, 385304 (2020).

The above citations are from Crossref's cited-by service (last updated successfully 2022-05-17 09:12:54) and SAO/NASA ADS (last updated successfully 2022-05-17 09:12:55). The list may be incomplete as not all publishers provide suitable and complete citation data.

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