Simplicial methods in the resource theory of contextuality
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912403690618880 |
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| author | Kharoof, Aziz Okay, Cihan |
| author_facet | Kharoof, Aziz Okay, Cihan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24010 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simplicial methods in the resource theory of contextuality Kharoof, Aziz Okay, Cihan Quantum Physics Algebraic Topology Category Theory 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. |
| title | Simplicial methods in the resource theory of contextuality |
| topic | Quantum Physics Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2505.24010 |