# From classical to quantum walk via erasure of which-way information

## TL;DR

This paper explores how erasing which-way information in a quantum walk can restore its ballistic, quantum behavior from a diffusive classical distribution, using a generalized quantum eraser approach.

## Contribution

It introduces a generalized quantum eraser scheme that enables erasure of which-way information in multi-coin quantum walks, recovering quantum ballistic features.

## Key findings

- Erasing which-way information restores ballistic quantum walk behavior.
- Complex erasure strategies can recover quantum features from classical distributions.
- The relation between information encoding and classicality is clarified.

## Abstract

Decoherence transforms a ballistic quantum walk into a diffusive classical random walk. After each step the environment measures the particle's path and the outside world gets to know the which-way information. The relation between the which-way information and the classicality of the spatial distribution is clearly visible in the multi-coin quantum walk in which the information about particle's path is encoded in the multi-coin degree of freedom. The more information is stored on the coins, the more classical and diffusive the spatial distribution is. Here, we propose a generalized version of the quantum eraser scenario that allows for complex erasure strategies. We show that the which-way information can be erased from the coins and the ballistic features in the spatial probability distribution can be recovered.