TY - JOUR

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

AU - Tate, Tatsuya

N1 - Funding Information:
∗The author is partially supported by JSPS Grant-in-Aid for Scientific Research (No. 21740117).

PY - 2013/6

Y1 - 2013/6

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 -