One-dimensional quantum walks via generating function and the CGMV method

Abstract

We treat a quantum walk (QW) on the line whose quantum coin at each vertex tends to be 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.

18 pages, 1 figure

References in corpus (2)

• Quantum recurrence of a subspace and operator-valued Schur functions
• Recurrence of biased quantum walks on a line

Cited by in corpus (1)

• Resolvent Methods for Quantum Walks with an Application to a Thue-Morse Quantum Walk