Homotopical approach to quantum contextuality
Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada
Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC, Canada
| Published: | 2020-01-05, volume 4, page 217 |
| Eprint: | arXiv:1905.03822v2 |
| Doi: | https://doi.org/10.22331/q-2020-01-05-217 |
| Citation: | Quantum 4, 217 (2020). |
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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.
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[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] Costantino Budroni, Adán Cabello, Otfried Gühne, Matthias Kleinmann, and Jan-Åke Larsson, "Kochen-Specker contextuality", Reviews of Modern Physics 94 4, 045007 (2022).
[6] 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).
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