Return Probability of Quantum and Correlated Random Walks |
| |
| Authors: | Chusei Kiumi Norio Konno Shunya Tamura |
| |
| Affiliation: | 1.Graduate School of Science and Engineering, Yokohama National University, Hodogaya, Yokohama 240-8501, Japan;2.Department of Applied Mathematics, Faculty of Engineering, Yokohama National University, Hodogaya, Yokohama 240-8501, Japan; |
| |
| Abstract: | The analysis of the return probability is one of the most essential and fundamental topics in the study of classical random walks. In this paper, we study the return probability of quantum and correlated random walks in the one-dimensional integer lattice by the path counting method. We show that the return probability of both quantum and correlated random walks can be expressed in terms of the Legendre polynomial. Moreover, the generating function of the return probability can be written in terms of elliptic integrals of the first and second kinds for the quantum walk. |
| |
| Keywords: | quantum walk correlated random walk return probability elliptic integral Legendre polynomial |
|
|
