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.

arXiv comment18 pages. Submitted Apr 7, 2026; no AI disclosures. Companion paper: arXiv:2609.30406 (geometric approach)