## Projectiles, rockets and quantum backflow

Consider a scenario where a non-relativistic one-dimensional quantum particle is prepared in some bounded region of space and left to propagate freely. After a certain amount time, we measure if the particle is in some distant target region. In this talk, I will prove the existence of `ultra-fast' initial quantum states, for which the probability of arrival is greater than that of any classical system prepared in the same region with the same momentum distribution.