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

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].

9 pages

References in corpus (5)

• Relationship Between Quantum Walk and Relativistic Quantum Mechanics
• Limit distributions of two-dimensional quantum walks
• Recurrence properties of unbiased coined quantum walks on infinite $d$-dimensional lattices
• Quantum random walks in one dimension
• Quantum walks and orbital states of a Weyl particle