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 (10)

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Cited by in corpus (3)

• Orthogonal Polynomials on the Unit Circle with Fibonacci Verblunsky Coefficients, II. Applications
• Localization of the Grover walks on spidernets and free Meixner laws
• Resolvent Methods for Quantum Walks with an Application to a Thue-Morse Quantum Walk