Stationary measure for two-state space-inhomogeneous quantum walk in one dimension

Abstract

We consider the two-state space-inhomogeneous coined quantum walk (QW) in one dimension. For a general setting, we obtain the stationary measure of the QW by solving the eigenvalue problem. As a corollary, stationary measures of the multi-defect model and space-homogeneous QW are derived. The former is a generalization of the previous works on one-defect model and the latter is a generalization of the result given by Konno and Takei (2015).

arXiv comment15 pages, revised version, Yokohama Mathematical Journal (in press)

References in corpus (5)

• Asymptotic evolution of quantum walks with random coin
• The stationary measure of a space-inhomogeneous quantum walk on the line
• Relation between two-phase quantum walks and the topological invariant
• Stationary measures of three-state quantum walks on the one-dimensional lattice
• Stationary measures for the three-state Grover walk with one defect in one dimension

Cited by in corpus (6)

• Eigenvalues of two-phase quantum walks with one defect in one dimension
• Generalized eigenfunctions for quantum walks via path counting approach
• Explicit expression of scattering operator of some quantum walks on impurities
• Strongly trapped space-inhomogeneous quantum walks in one dimension
• Localization in quantum walks with periodically arranged coin matrices
• A discontinuity of the energy of quantum walk in impurities