Resonant-tunneling in discrete-time quantum walk

TL;DR

This paper demonstrates that discrete-time quantum walks on the line exhibit quantum tunneling, allowing walkers to pass through barriers with high probability, a phenomenon absent in classical random walks.

Contribution

It reveals a novel tunneling property in discrete-time quantum walks, distinct from classical behaviors and other quantum phenomena like spreading and localization.

Findings

Quantum walkers can tunnel through double-wells with probability 1.

Quantum tunneling in walks differs from classical random walk behavior.

This tunneling property is unique to quantum walks and not observed in classical systems.

Abstract

We show that discrete-time quantum walks on the line, $\mathbb{Z}$, behave as "the quantum tunneling". In particular, quantum walkers can tunnel through a double-well with the transmission probability $1$ under a mild condition. This is a property of quantum walks which cannot be seen on classical random walks, and is different from both linear spreadings and localizations.