Localization of discrete time quantumwalks on the glued trees

Yusuke Ide, Norio Konno, Etsuo Segawa, Xin Ping Xu

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

In this paper, we consider the time averaged distribution of discrete time quantum walks on the glued trees. In order to analyze the walks on the glued trees, we consider a reduction to the walks on path graphs. Using a spectral analysis of the Jacobi matrices defined by the corresponding random walks on the path graphs, we have a spectral decomposition of the time evolution operator of the quantum walks. We find significant contributions of the eigenvalues, ±1, of the Jacobi matrices to the time averaged limit distribution of the quantum walks. As a consequence, we obtain the lower bounds of the time averaged distribution.

Original languageEnglish
Pages (from-to)1501-1514
Number of pages14
JournalEntropy
Volume16
Issue number3
DOIs
Publication statusPublished - 2014 Mar

Keywords

  • Chebyshev polynomial
  • Discrete time quantum walks
  • Glued tree
  • Jacobi matrix
  • Localization
  • Orthogonal polynomial
  • Spectral analysis

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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