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arXiv · 1212.1109

Weak limits for quantum walks on the half-line

Chaobin Liu·Nelson Petulante
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Abstract

For a discrete two-state quantum walk (QW) on the half-line with a general condition at the boundary, we formulate and prove a weak limit theorem describing the terminal behavior of its transition probabilities. In this context, localization is possible even for a walk predicated on the assumption of homogeneity. For the Hadamard walk on the half-line, the weak limit is shown to be independent of the initial coin state and to exhibit no localization.

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Chaobin Liu, Nelson Petulante. 2012-12-05. Weak limits for quantum walks on the half-line. https://doi.org/10.1142/s0219749913500548

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