A New Limit Theorem for Quantum Walk in Terms of Quantum Bernoulli Noises

In this paper, we consider limit probability distributions of the quantum walk recently introduced by Wang and Ye (C.S. Wang and X.J. Ye, Quantum walk in terms of quantum Bernoulli noises, Quantum Inf. Process. 15 (2016), no. 5, 1897–1908). We first establish several technical theorems, which themse...

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Autores principales: Wang, Caishi, Ren, Suling, Tang, Yuling
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516969/
https://www.ncbi.nlm.nih.gov/pubmed/33286259
http://dx.doi.org/10.3390/e22040486
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author Wang, Caishi
Ren, Suling
Tang, Yuling
author_facet Wang, Caishi
Ren, Suling
Tang, Yuling
author_sort Wang, Caishi
collection PubMed
description In this paper, we consider limit probability distributions of the quantum walk recently introduced by Wang and Ye (C.S. Wang and X.J. Ye, Quantum walk in terms of quantum Bernoulli noises, Quantum Inf. Process. 15 (2016), no. 5, 1897–1908). We first establish several technical theorems, which themselves are also interesting. Then, by using these theorems, we prove that, for a wide range of choices of the initial state, the above-mentioned quantum walk has a limit probability distribution of standard Gauss type, which actually gives a new limit theorem for the walk.
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spelling pubmed-75169692020-11-09 A New Limit Theorem for Quantum Walk in Terms of Quantum Bernoulli Noises Wang, Caishi Ren, Suling Tang, Yuling Entropy (Basel) Article In this paper, we consider limit probability distributions of the quantum walk recently introduced by Wang and Ye (C.S. Wang and X.J. Ye, Quantum walk in terms of quantum Bernoulli noises, Quantum Inf. Process. 15 (2016), no. 5, 1897–1908). We first establish several technical theorems, which themselves are also interesting. Then, by using these theorems, we prove that, for a wide range of choices of the initial state, the above-mentioned quantum walk has a limit probability distribution of standard Gauss type, which actually gives a new limit theorem for the walk. MDPI 2020-04-24 /pmc/articles/PMC7516969/ /pubmed/33286259 http://dx.doi.org/10.3390/e22040486 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Wang, Caishi
Ren, Suling
Tang, Yuling
A New Limit Theorem for Quantum Walk in Terms of Quantum Bernoulli Noises
title A New Limit Theorem for Quantum Walk in Terms of Quantum Bernoulli Noises
title_full A New Limit Theorem for Quantum Walk in Terms of Quantum Bernoulli Noises
title_fullStr A New Limit Theorem for Quantum Walk in Terms of Quantum Bernoulli Noises
title_full_unstemmed A New Limit Theorem for Quantum Walk in Terms of Quantum Bernoulli Noises
title_short A New Limit Theorem for Quantum Walk in Terms of Quantum Bernoulli Noises
title_sort new limit theorem for quantum walk in terms of quantum bernoulli noises
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516969/
https://www.ncbi.nlm.nih.gov/pubmed/33286259
http://dx.doi.org/10.3390/e22040486
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