  We study the quantum diffusion of an electron in a quantum chain starting
from an initial state localized around a given site. As the wavepacket
diffuses, the probability of reconstructing the initial state on another site
diminishes drastically with the distance. In order to optimize the state
transmission we find that a topological quantum phase can be introduced. The
effect of this phase is the reduction of wavepacket spreading together with
almost coherent group propagation. In this regime, the electron has a
quasi-linear dispersion and high fidelity can be achieved also over large
distances in terms of lattice spacing.
