Nakayama's reduction of quantum topos and Bayesian quantum computing

Abstract:Nakayama found the way to limit the contexts in the Döring-Isham topos quantum theory and unified such limitation and the definition of probability as a single choice of topology. We explain how this unification supports the Bayesian perspective where the probability changes as data is obtained. We describe this change as a local shift of the applicability of a predictive theory and apply it to quantum computing.

18 pages. Submitted Apr 7, 2026; no AI disclosures. Companion paper: arXiv:2609.30406 (geometric approach)

Quantum Physics (quant-ph); Mathematical Physics (math-ph); Category Theory (math.CT)

arXiv:2609.34200 [quant-ph]

(or arXiv:2609.34200v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.34200 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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