Uniform mixing and $ε$-uniform mixing on cycles

• URL: http://arxiv.org/abs/2607.04207v1
• Date: Sun, 05 Jul 2026 09:56:05 GMT
• Title: Uniform mixing and $ε$-uniform mixing on cycles
• Abstract summary: We study continuous-time quantum walks on cycles.<n>For every prime $p2$, we show that the cycle $C_p2$ admits $$-uniform mixing.
• Score: 6.617487928813374
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study continuous-time quantum walks on cycles. We prove two complementary results. Firstly, the cycle $C_9$ does not admit uniform mixing at any time. Using the similar idea and Dickson polynomials, we prove that $C_{15}$ does not admit uniform mixing at any time neither. Secondly, for every prime $p$, we show that the cycle $C_{p^2}$ admits $ε$-uniform mixing.

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