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

Authors:
Norio Konno;Etsuo Segawa
Affiliations:
Department of Applied Mathematics, Faculty of Engineering, Yokohama National University, Yokohama, Japan;Department of Value and Decision Science, Tokyo Institute of Technology, Tokyo, Japan
Venue:
Quantum Information & Computation
Year:
2011

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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].