### Abstract

We treat quantum walk (QW) on the line whose quantum coin at each vertex tends to the identity as the distance goes to infinity. We obtain a limit theorem that this QW exhibits localization with not an exponential but a "power-law" decay around the origin and a "strongly" ballistic spreading called bottom localization in this paper. This limit theorem implies the weak convergence with linear scaling whose density has two delta measures at x = 0 (the origin) and x = 1 (the bottom) without continuous parts.

Original language | English |
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Pages (from-to) | 1165-1186 |

Number of pages | 22 |

Journal | Quantum Information and Computation |

Volume | 14 |

Issue number | 13-14 |

Publication status | Published - 2014 Oct 1 |

### Keywords

- CMV matrix
- Generating function
- Quantum walk

### ASJC Scopus subject areas

- Theoretical Computer Science
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Computational Theory and Mathematics

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## Cite this

Konno, N., & Segawa, E. (2014). One-dimensional quantum walks via generating function and the CGMV method.

*Quantum Information and Computation*,*14*(13-14), 1165-1186.