Limit theorems for decoherent two dimensional quantum walks

Amanda C. Oliveira

Shimpei ENDO, Takako Endo, Norio Konno +2 more

We attempt to analyze a one-dimensional space-inhomogeneous quantum walk (QW) with one defect at the origin, which has two different quantum coins in positive and negative parts. We call the QW ``the two-phase QW with one defect'', which we treated concerning localization theorems. The two-phase QW with one defect has been expected to be a mathematical model of topological insulator which is an intense issue both theoretically and experimentally. In this paper, we derive the weak limit theorem describing the ballistic spreading, and as a result, we obtain the mathematical expression of the whole picture of the asymptotic behavior. Our approach is based mainly on the generating function of the weight of the passages. We emphasize that the time-averaged limit measure is symmetric for the origin, however, the weak limit measure is asymmetric, which implies that the weak limit theorem represents the asymmetry of the probability distribution.

Norio Konno, Hyun Jae Yoo

Toru Fuda, Daiju Funakawa, Akito Suzuki

This paper proves a weak limit theorem for a one-dimensional split-step quantum walk and investigates the limit density function. In the density function, the difference between two Konno's functions appears.

Viv M. Kendon, Ben Tregenna

Masaya Maeda, Hironobu Sasaki, Etsuo Segawa +2 more