Nakayama's reduction of quantum topos and Bayesian quantum computing

Atsuhide Mori

Home/Archive/arXiv

arXiv · 2609.34200

Nakayama's reduction of quantum topos and Bayesian quantum computing

Atsuhide Mori

View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

quant-ph math-ph math.CT math.MP

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Atsuhide Mori. 2026-09-28. Nakayama's reduction of quantum topos and Bayesian quantum computing. https://arxiv.org/abs/2609.34200

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Spectral moments and entropy rigidity of quantum channels: a three-mode photonic witness

Majorization and von Neumann entropy provide related but inequivalent descriptions of spectral disorder in quantum optical states. We investigate the channels preserving these descriptions and propose a three-mode photonic test of their difference. For channels with equal input and output dimensions, we show that constant output purity and third spectral moment on the unitary orbit of one simple-spectrum state determine the majorization-preserving channel forms, without assuming unitality.For qubits, output purity alone is sufficient. Preservation of entropy equality is substantially more restrictive: in dimension $d\geqslant3$, even a local condition near the maximally mixed state permits only replacement and unitary channels. Qubits admit an additional depolarizing family, but this exception disappears under extension by an idle auxiliary qubit. We construct exactly entropy-matched qutrit inputs whose output entropies split at cubic order under nontrivial depolarizing noise. A proposed single-photon implementation uses three optical modes, randomized Weyl transformations and population or spectral-moment measurements.Explicit expressions are also obtained for preparation mismatch,readout uncertainty and input-independent loss. The results connect quadratic and cubic spectral information with experimentally interpretable tests of quantum-channel structure.

quant-ph↗

arXiv2026

Spectral diffusion of phosphorus donors in silicon at high magnetic field

We study the central spin physics of a phosphorus donor electron in silicon interacting with a silicon-29 bath at high magnetic field (8.59 T). We find that the spectral diffusion time is shorter and exhibits a larger anisotropy with respect to crystal orientation in the magnetic field than in previous measurements at 0.35 T. The increased anisotropy suggests a modification of the hyperfine interactions at high field. The 1.2 THz cyclotron energy is a significant fraction of the 10.8 THz Rydberg energy of the bound donor, which can result in a non-trivial magnetic perturbation of the hydrogenic donor wavefunction. Low-power, above-bandgap optical excitation is seen to increase the spectral diffusion time, recovering the low-field spectral diffusion time at most crystal orientations. Understanding such perturbations to the spatial wavefunction of donor electron spins could be key to engineering their high-fidelity control.

quant-ph↗

arXiv2026

Many-Body Bound States in the Continuum

A bound state in the continuum (BIC) is a spatially localized energy eigenstate embedded in a continuous spectrum of extended eigenstates. While diverse types of single-particle BICs have been reported in the literature, whether such states can exist in genuinely many-body systems remains an open question. Here, we present numerical evidence and a perturbative analysis supporting the existence of many-body BICs in a one-dimensional Bose-Hubbard chain with an attractive impurity potential, a system previously known to host a BIC in the two-particle sector. Furthermore, we demonstrate that the Bethe-type construction of the known two-particle BIC breaks down already for three particles even for arbitrary finite superpositions of Bethe waves. The resulting BICs violate the eigenstate thermalization hypothesis for several local one- and two-body observables, leading to nonthermal dynamics from experimentally accessible initial states.

quant-ph↗