A Spectral Analysis of Discrete-Time Quantum Walks Related to the Birth and Death Chains

Choon Lin Ho, Yusuke Ide, Norio Konno, Etsuo Segawa, Kentaro Takumi

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, we consider a spectral analysis of discrete time quantum walks on the path. For isospectral coin cases, we show that the time averaged distribution and stationary distributions of the quantum walks are described by the pair of eigenvalues of the coins as well as the eigenvalues and eigenvectors of the corresponding random walks which are usually referred as the birth and death chains. As an example of the results, we derive the time averaged distribution of so-called Szegedy’s walk which is related to the Ehrenfest model. It is represented by Krawtchouk polynomials which is the eigenvectors of the model and includes the arcsine law.

Original languageEnglish
Pages (from-to)207-219
Number of pages13
JournalJournal of Statistical Physics
Volume171
Issue number2
DOIs
Publication statusPublished - 2018 Apr 1

Keywords

  • Birth and death chain
  • Ehrenfest model
  • Krawtchouk polynomials
  • Quantum walk

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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