  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].
