  We investigate the transport properties and entanglement between spin and
position of one-dimensional quantum walks starting from a qubit over position
states following a delta-like (local state) and Gaussian (delocalized state)
distributions. We find out that if the initial state is delocalized enough and
a NOT gate reflects this state backwards, then the interference pattern
extinguishes the position dispersion without preventing the propagation of the
state. This effect allows the creation of a Trojan wave packet, a non-spreading
and non-stationary double-peak quantum state.
