Arithmetic of Bohr Frequencies Governs Uniform Mixing in Randomly Timed Quantum Spin Chains
Year: 2026
Type: preprint
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 $N\ge2$ spins, this is possible when $N+1$ is a power of two, a prime, or twice a prime. It is impossible when $15\mid(N+1)$, $21\mid(N+1)$, or $6\mid(N+1)$ with $N\ge11$. 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.
Source: arXiv (Cornell University)
Author: Kang, Musung
Institution: Seoul National University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213365389