Simplicial quantum contextuality

• URL: http://arxiv.org/abs/2204.06648v4
• Date: Tue, 16 May 2023 19:40:08 GMT
• Title: Simplicial quantum contextuality
• Authors: Cihan Okay, Aziz Kharoof, Selman Ipek
• Abstract summary: We introduce a new framework for contextuality based on simplicial sets, models of topological spaces that play a prominent role in homotopy theory. Our approach extends measurement scenarios to consist of spaces (rather than sets) of measurements and outcomes. We present a topologically inspired new proof of Fine's theorem for characterizing noncontextuality in Bell scenarios.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a new framework for contextuality based on simplicial sets, combinatorial models of topological spaces that play a prominent role in modern homotopy theory. Our approach extends measurement scenarios to consist of spaces (rather than sets) of measurements and outcomes, and thereby generalizes nonsignaling distributions to simplicial distributions, which are distributions on spaces modeled by simplicial sets. Using this formalism we present a topologically inspired new proof of Fine's theorem for characterizing noncontextuality in Bell scenarios. Strong contextuality is generalized suitably for simplicial distributions, allowing us to define cohomological witnesses that extend the earlier topological constructions restricted to algebraic relations among quantum observables to the level of probability distributions. Foundational theorems of quantum theory such as the Gleason's theorem and Kochen-Specker theorem can be expressed naturally within this new language.

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