Universal dynamical scaling laws in three-state quantum walks

Abstract

We perform a finite-time scaling analysis over the detrapping point of a three-state quantum walk on the line. The coin operator is parameterized by ρ that controls the wavepacket spreading velocity. The input state prepared at the origin is set as symmetric linear combination of two eigenstates of the coin operator with a characteristic mixing angle θ, one of them being the component that results in full spreading occurring at θc(ρ) for which no fraction of the wavepacket remains trapped near the initial position. We show that relevant quantities such as the survival probability and the participation ratio assume single parameter scaling forms at the vicinity of the detrapping angle θc. In particular, we show that the participation ratio grows linearly in time with a logarithmic correction, thus shedding light on previous reports of sublinear behavior.

Localization of space-inhomogeneous three-state quantum walks

“…The research on quantum walks (QWs) began in the early 2000s [1,2], and QWs play important roles in various fields, and a variety of QW models have been analyzed theoretically and numerically. This paper focuses on the mathematical analysis of discrete-time three-state QWs on the integer lattice, studied intensively by [3][4][5][6][7][8][9]. Three-state QWs have an interesting property called localization, where the probability of finding the particle around the initial position remains positive in the long-time limit.…”

Localization of space-inhomogeneous three-state quantum walks

“…The research on quantum walks (QWs) began in the early 2000s [1,2,3], and QWs play important roles in various fields, and various types of QWs have been analyzed theoretically and numerically. This paper focuses on the mathematical analysis of discretetime three-state QWs on the integer lattice, which is studied intensively by [4,5,6,7,8,9,10]. Three-state QWs have an interesting property called localization, where the probability of finding the particle around the initial position remains positive in the longtime limit.…”

Localization in quantum walks with periodically arranged coin matrices

“…The study of quantum walks, which began in the early 2000s [1,2], has spread and attracted much attention, especially for its applications in quantum information [3,4,5,6,7,8]. One of the most characteristic properties of the quantum walk is localization, an essential property for manipulating particles.…”