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arXiv · 2606.27740

Bottleneck Effects and Harmonic-Type Velocity Bounds for Periodic Quantum Walks

Houssam Abdul-Rahman·Thomas A. Jackson·Darren C. Ong
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Abstract

We prove explicit upper bounds on the propagation velocity of one-dimensional quantum walks with periodic coins of arbitrary period. We treat two complementary settings. First, in a perturbative regime where one transmission parameter is small, we show that the corresponding almost reflecting coin acts as a bottleneck for transport: the velocity is bounded linearly in this parameter, with an explicit leading order estimate. Second, for arbitrary nonzero transmission parameters, we prove a general a priori bound in terms of their harmonic mean, together with a refined version that detects the spatial variation of neighboring coins. Moreover, we prove a general lower bound on the velocity. These bounds apply directly to the corresponding CMV setting.

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Houssam Abdul-Rahman, Thomas A. Jackson, Darren C. Ong. 2026-06-26. Bottleneck Effects and Harmonic-Type Velocity Bounds for Periodic Quantum Walks. https://arxiv.org/abs/2606.27740

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