PreprintarXiv licencearXiv
Arithmetic of Bohr Frequencies Governs Uniform Mixing in Randomly Timed Quantum Spin Chains
Abstract
Randomizing the readout time averages the mode interference in a quantum walk. We ask when this makes the site populations of a uniformly coupled XY chain exactly uniform for every initial site. For N≥2 spins, this is possible when N+1 is a power of two, a prime, or twice a prime. It is impossible when 15|(N+1), 21|(N+1), or 6|(N+1) with N≥11. Uniformity uniquely fixes the averaged cosine coherences according to the mirror parities of the modes. Equal Bohr frequencies can impose incompatible coherence values. We classify these parity collisions using vanishing sums of roots of unity and prove existence in the positive cases through a phase distribution on a torus.
Related
- Thicker Is Better: How Surfactant Viscosity Governs Uniform Surfactant Lung Delivery
- Homological Thresholds in Randomly Monitored Quantum Error-Correcting Codes
- When irrelevance governs: dissipation-regression scaling in open quantum criticality
- Cumulative locality governs collective quantum charging
- Coherence Rather Than Error Rate Governs Privacy in Multi-Tenant Quantum Computing
BibTeX
@misc{kang2026arithmetic,
title = {{Arithmetic of Bohr Frequencies Governs Uniform Mixing in Randomly Timed Quantum Spin Chains}},
author = {Musung Kang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14463},
eprint = {2609.14463},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14463},
}
RIS
TY - UNPB
TI - Arithmetic of Bohr Frequencies Governs Uniform Mixing in Randomly Timed Quantum Spin Chains
AU - Musung Kang
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14463
UR - https://arxiv.org/abs/2609.14463
AB - Randomizing the readout time averages the mode interference in a quantum walk. We ask when this makes the site populations of a uniformly coupled XY chain exactly uniform for every initial site. For N≥2 spins, this is possible when N+1 is a power of two, a prime, or twice a prime. It is impossible when 15|(N+1), 21|(N+1), or 6|(N+1) with N≥11. Uniformity uniquely fixes the averaged cosine coherences according to the mirror parities of the modes. Equal Bohr frequencies can impose incompatible coherence values. We classify these parity collisions using vanishing sums of roots of unity and prove existence in the positive cases through a phase distribution on a torus.
ER -