Localization of discrete-time quantum walks on a half line via the CGMV method

Norio Konno, Etsuo Segawa

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)

Abstract

We study discrete-time quantum walks on a half line by means of spectral analysis. Cantero et al. [1] showed that the CMV matrix, which gives a recurrence relation for the orthogonal Laurent polynomials on the unit circle [2], expresses the dynamics of the quantum walk. Using the CGMV method introduced by them, the name is taken from their initials, we obtain the spectral measure for the quantum walk. As a corollary, we give another proof for localization of the quantum walk on homogeneous trees shown by Chisaki et al. [3].

Original languageEnglish
Pages (from-to)485-495
Number of pages11
JournalQuantum Information and Computation
Volume11
Issue number5-6
Publication statusPublished - 2011 May 1

Keywords

  • CMV matrix
  • Localization
  • Quantum walk

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Computational Theory and Mathematics

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