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

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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.

Original languageEnglish
Article number1350018
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Volume16
Issue number2
DOIs
Publication statusPublished - 2013 Jun 1

Keywords

  • Quantum walks
  • weak limit theorem

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Mathematical Physics
  • Applied Mathematics

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