An algebraic structure for one-dimensional quantum walks and a new proof of the weak limit theorem

Tatsuya Tate

doi:10.1142/S0219025713500185

An algebraic structure for one-dimensional quantum walks and a new proof of the weak limit theorem

Tatsuya Tate

理学研究科・数学専攻

研究成果: Article › 査読

1 被引用数 (Scopus)

抄録

An algebraic structure for one-dimensional quantum walks is introduced. This structure characterizes, in some sense, one-dimensional quantum walks. A natural computation using this algebraic structure leads us to obtain an effective formula for the characteristic function of the transition probability. Then, the weak limit theorem for the transition probability of quantum walks is deduced by using simple properties of the Chebyshev polynomials.

本文言語	English
論文番号	1350018
ジャーナル	Infinite Dimensional Analysis, Quantum Probability and Related Topics
巻	16
号	2
DOI	https://doi.org/10.1142/S0219025713500185
出版ステータス	Published - 2013 6 1

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Mathematical Physics
Applied Mathematics

文献へのアクセス

10.1142/S0219025713500185

フィンガープリント「An algebraic structure for one-dimensional quantum walks and a new proof of the weak limit theorem」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル

@article{ebf33c99c7b94b47a715ab79351553da,

title = "An algebraic structure for one-dimensional quantum walks and a new proof of the weak limit theorem",

abstract = "An algebraic structure for one-dimensional quantum walks is introduced. This structure characterizes, in some sense, one-dimensional quantum walks. A natural computation using this algebraic structure leads us to obtain an effective formula for the characteristic function of the transition probability. Then, the weak limit theorem for the transition probability of quantum walks is deduced by using simple properties of the Chebyshev polynomials.",

keywords = "Quantum walks, weak limit theorem",

author = "Tatsuya Tate",

year = "2013",

month = jun,

day = "1",

doi = "10.1142/S0219025713500185",

language = "English",

volume = "16",

journal = "Infinite Dimensional Analysis, Quantum Probability and Related Topics",

issn = "0219-0257",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "2",

}

TY - JOUR

T1 - An algebraic structure for one-dimensional quantum walks and a new proof of the weak limit theorem

AU - Tate, Tatsuya

PY - 2013/6/1

Y1 - 2013/6/1

N2 - An algebraic structure for one-dimensional quantum walks is introduced. This structure characterizes, in some sense, one-dimensional quantum walks. A natural computation using this algebraic structure leads us to obtain an effective formula for the characteristic function of the transition probability. Then, the weak limit theorem for the transition probability of quantum walks is deduced by using simple properties of the Chebyshev polynomials.

AB - An algebraic structure for one-dimensional quantum walks is introduced. This structure characterizes, in some sense, one-dimensional quantum walks. A natural computation using this algebraic structure leads us to obtain an effective formula for the characteristic function of the transition probability. Then, the weak limit theorem for the transition probability of quantum walks is deduced by using simple properties of the Chebyshev polynomials.

KW - Quantum walks

KW - weak limit theorem

UR - http://www.scopus.com/inward/record.url?scp=84880565714&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880565714&partnerID=8YFLogxK

U2 - 10.1142/S0219025713500185

DO - 10.1142/S0219025713500185

M3 - Article

AN - SCOPUS:84880565714

VL - 16

JO - Infinite Dimensional Analysis, Quantum Probability and Related Topics

JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics

SN - 0219-0257

IS - 2

M1 - 1350018

ER -