Entropy 2014, 16(3), 1501-1514; doi:10.3390/e16031501

Localization of Discrete Time Quantum Walks on the Glued Trees

1,* email, 2email, 3email and 4,5email
Received: 4 December 2013; in revised form: 15 January 2014 / Accepted: 10 March 2014 / Published: 18 March 2014
(This article belongs to the Special Issue Advances in Information Theory)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
Keywords: discrete time quantum walks; Localization; glued tree; Jacobi matrix; spectral analysis; Orthogonal Polynomial; Chebyshev polynomial
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MDPI and ACS Style

Ide, Y.; Konno, N.; Segawa, E.; Xu, X.-P. Localization of Discrete Time Quantum Walks on the Glued Trees. Entropy 2014, 16, 1501-1514.

AMA Style

Ide Y, Konno N, Segawa E, Xu X-P. Localization of Discrete Time Quantum Walks on the Glued Trees. Entropy. 2014; 16(3):1501-1514.

Chicago/Turabian Style

Ide, Yusuke; Konno, Norio; Segawa, Etsuo; Xu, Xin-Ping. 2014. "Localization of Discrete Time Quantum Walks on the Glued Trees." Entropy 16, no. 3: 1501-1514.

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