Quantum Random Walks in One Dimension
Quantum Information Processing
Analytic Combinatorics
One-dimensional discrete-time quantum walks on random environments
Quantum Information Processing
Localization of an inhomogeneous discrete-time quantum walk on the line
Quantum Information Processing
Localization of discrete-time quantum walks on a half line via the CGMV method
Quantum Information & Computation
Limit theorems for quantum walks with memory
Quantum Information & Computation
Limit theorems for the discrete-time quantum walk on a graph with joined half lines
Quantum Information & Computation
The CGMV method for quantum walks
Quantum Information Processing
Quantum walks: a comprehensive review
Quantum Information Processing
Realization of the probability laws in the quantum central limit theorems by a quantum walk
Quantum Information & Computation
Hi-index | 0.00 |
We treat three types of measures of the quantum walk (QW) with the spatial perturbation at the origin, which was introduced by Konno (Quantum Inf Proc 9:405, 2010): time averaged limit measure, weak limit measure, and stationary measure. From the first two measures, we see a coexistence of the ballistic and localized behaviors in the walk as a sequential result following (Konno in Quantum Inf Proc 9:405, 2010; Quantum Inf Proc 8:387---399, 2009). We propose a universality class of QWs with respect to weak limit measure. It is shown that typical spatial homogeneous QWs with ballistic spreading belong to the universality class. We find that the walk treated here with one defect also belongs to the class. We mainly consider the walk starting from the origin. However when we remove this restriction, we obtain a stationary measure of the walk. As a consequence, by choosing parameters in the stationary measure, we get the uniform measure as a stationary measure of the Hadamard walk and a time averaged limit measure of the walk with one defect respectively.