Simplicial methods in the resource theory of contextuality

Aziz Kharoof; Cihan Okay

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arXiv · 2505.24010

Simplicial methods in the resource theory of contextuality

Aziz Kharoof·Cihan Okay

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Abstract

We develop a resource theory of contextuality within the framework of symmetric monoidal categories, extending recent simplicial approaches to quantum contextuality. Building on the theory of simplicial distributions, which integrates homotopy-theoretic structures with probability, we introduce event scenarios as a functorial generalization of presheaf-theoretic measurement scenarios and prove their equivalence to bundle scenarios via the Grothendieck construction. We define symmetric monoidal structures on these categories and extend the distribution functor to a stochastic setting, yielding a resource theory that generalizes the presheaf-theoretic notion of simulations. Our main result characterizes convex maps between simplicial distributions in terms of non-contextual distributions on a corresponding mapping scenario, enhancing and extending prior results in categorical quantum foundations.

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Aziz Kharoof, Cihan Okay. 2025-05-29. Simplicial methods in the resource theory of contextuality. https://arxiv.org/abs/2505.24010

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