Boomerang quantum walks

TL;DR

This paper explores the quantum boomerang effect in discrete-time quantum walks with random phase disorder, revealing how initial states and coin parameters influence quantum transport and localization behaviors.

Contribution

It demonstrates that the quantum boomerang effect can emerge solely from intrinsic momentum dynamics without external bias, and identifies key scaling laws related to initial state and disorder strength.

Findings

Quantum boomerang effect depends on initial state choices.

Maximum mean position scales as $ heta^{-2}$ near the Pauli-Z coin.

Localization length scales with disorder as $W^{-2}$.

Abstract

In this study, we investigate the emergence of the quantum boomerang effect in discrete-time quantum walks (DTQWs) subjected to random phase disorder. Our analysis shows that this effect can arise solely from the intrinsic momentum dynamics of the DTQW, without requiring external bias or asymmetry. We explore the evolution of the mean position of the quantum walker, denoted as $\overline{X}(t)$, under various initial conditions of the walker and quantum coin operators. The results indicate a significant dependence of the observed phenomena on the choice of initial state, enabling the selective induction of the quantum boomerang effect in both or only one portion of the wavepacket associated with specific internal states. By varying the quantum coin parameter $\theta$, we find that the maximum mean position follows a power-law decay near the Pauli-Z coin, characterized by $X_{\text{Max}} \sim \theta^{-2}$. Additionally, we identify a scaling behavior $X_{\text{Max}} \sim W^{-2}$, which is consistent with the localization length observed in disordered quantum systems. Such a selective nature of the boomerang effect related to internal states reveals valuable insights for controlling quantum transport, which could lead to applications in quantum state management, spatial separation of quantum information carriers, and targeted information retrieval.