Quantum walks with an anisotropic coin II: scattering theory

We perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum walks that we consider include one-defect models, two-phase quantum walks, and topological phase quantum walks as speci...

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Bibliographic Details
Published in:arXiv.org 2018-01
Main Authors: Richard, S, Suzuki, A, R Tiedra de Aldecoa
Format: Article
Language:English
Subjects:
Anisotropy
Hilbert space
Random walk theory
Scattering
Online Access:Get full text
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Summary:We perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum walks that we consider include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. Our analysis is based on an abstract framework for the scattering theory of unitary operators in a two-Hilbert spaces setting, which is of independent interest.
ISSN:2331-8422
DOI:10.48550/arxiv.1801.02779