English

Weak limits for quantum walks on the half-line

Quantum Physics 2015-10-05 v3 Mathematical Physics math.MP Probability

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.

Keywords

Cite

@article{arxiv.1212.1109,
  title  = {Weak limits for quantum walks on the half-line},
  author = {Chaobin Liu and Nelson Petulante},
  journal= {arXiv preprint arXiv:1212.1109},
  year   = {2015}
}

Comments

Added references and some other updates, corrected typos

R2 v1 2026-06-21T22:49:17.275Z