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

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