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

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.