Twisted simplicial distributions
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914733037191168 |
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| author | Okay, Cihan Stern, Walker H. |
| author_facet | Okay, Cihan Stern, Walker H. |
| contents | We introduce a theory of twisted simplicial distributions on simplicial principal bundles, which allow us to capture Bell's non-locality, and the more general notion of quantum contextuality. We leverage the classical theory of simplicial principal bundles, as well as structures on categories of such bundles, to provide powerful computational tools for analyzing twisted distributions in terms of both direct constructions in simplicial sets and techniques from homological algebra. We use these techniques to analyze our key examples: quantum distributions and operator-theoretic polytopes used in the classical simulation of quantum computation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19808 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted simplicial distributions Okay, Cihan Stern, Walker H. Quantum Physics Algebraic Topology Category Theory We introduce a theory of twisted simplicial distributions on simplicial principal bundles, which allow us to capture Bell's non-locality, and the more general notion of quantum contextuality. We leverage the classical theory of simplicial principal bundles, as well as structures on categories of such bundles, to provide powerful computational tools for analyzing twisted distributions in terms of both direct constructions in simplicial sets and techniques from homological algebra. We use these techniques to analyze our key examples: quantum distributions and operator-theoretic polytopes used in the classical simulation of quantum computation. |
| title | Twisted simplicial distributions |
| topic | Quantum Physics Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2403.19808 |