Stationary measures of three-state quantum walks on the one-dimensional lattice
arXiv:1702.01523
Abstract
In this paper, we consider stationary measures of discrete-time three-state quantum walks including the Fourier and Grover walks in the one-dimensional lattice. We give non-uniform stationary measures by solving the corresponding eigenvalue problem. Our new method is based on a reduced matrix, which is different from the generating function approach in our previous work. As a corollary, the Fourier walk on the cycle has a stationary measure with a periodicity.
arXiv comment10 pages
References in corpus (7)
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Cited by in corpus (7)
- Eigenvalues of two-phase quantum walks with one defect in one dimension
- Stationary measure for two-state space-inhomogeneous quantum walk in one dimension
- Localization of space-inhomogeneous three-state quantum walks
- Strongly trapped space-inhomogeneous quantum walks in one dimension
- Localization in quantum walks with periodically arranged coin matrices
- Uniform stationary measure of space-inhomogeneous quantum walks in one dimension
- Stationary amplitudes of quantum walks on the higher-dimensional integer lattice