Quantum walk in terms of quantum Bernoulli noise and quantum central limit theorem for quantum Bernoulli noise
type: Item
instance of: scholarly article
title: Quantum walk in terms of quantum Bernoulli noise and quantum central limit theorem for quantum Bernoulli noise
zbMATH Open document ID: 1404.81157
DOI: 10.1155/2018/2507265
author: Ce Wang
author: Yuling Tang
author: Suling Ren
author: Caishi Wang
published in: Advances in Mathematical Physics
publication date: 2018-12-11T00:00:00Z
review text: Summary: As a unitary quantum walk with infinitely many internal degrees of freedom, the quantum walk in terms of quantum Bernoulli noise (recently introduced by Wang and Ye) shows a rather classical asymptotic behavior, which is quite different from the case of the usual quantum walks with a finite number of internal degrees of freedom. In this paper, we further examine the structure of the walk. By using the Fourier transform on the state space of the walk, we obtain a formula that links the moments of the walk's probability distributions directly with annihilation and creation operators on Bernoulli functionals. We also prove some other results on the structure of the walk. Finally, as an application of these results, we establish a quantum central limit theorem for the annihilation and creation operators themselves.
Mathematics Subject Classification ID: 81S25
Mathematics Subject Classification ID: 81R15
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 6991940
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/2507265
OpenAlex ID: W2789223459
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description: scientific article; zbMATH DE number 6991940