Title
"Symmetry of localization and weak limit measure for quantum walk with two phases"
Takako Watanabe (Ochanomizu University)
Abstract
We treat a position dependent quantum walk (QW) model with two parameters. We assign two different quantum coins to positive and negative parts respectively. We call the model ``two-phase QW model''. We obtain two kinds of limit theorems for the QW model. One is the time averaged limit measure corresponding to localization. Second one is the weak limit measure corresponding to the ballistic spreading. The analytical method is mainly based on the generating function for the weight of passages. It is the first results on localization and weak limit theorem for two-phase QW model. The first result implies that localization for the QW can be expressed by the time-averaged limit measure for the model. Our explicit expression for the time-averaged limit measure ensures localization for any initial coin state. Moreover, the time-averaged limit measure has a starting point symmetry also for any initial coin state. On the other hand, the weak limit theorem, the second result, shows the asymmetricity of the probability distribution depending on the initial coin state.
