Limit distribution of a quantum walk driven by a CMV matrix
Takuya Machida · arXiv (Cornell University) · 2019
Quantum walks with CMV matrices, five-diagonal unitary matrices, started to be studied in 2003 [1]. The spectral analysis for CMV matrices told us that the quantum walks could localize in distribution depending on the Verblunsky parameters of the matrices. In this paper, we work on a quantum walk whose system is manipulated by a CMV matrix with homogeneous Vervlunsky parameters, and present long-time limit distributions. One can understand from the theory that the quantum walk does not localize and how it approximately distributes after the long-time evolution has been executed on the walk.