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)
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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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