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.Keywords Spreading · Entanglement · Gaussian states · Quantum walks 1 IntroductionFrom the epic poem Iliad, the term "Trojan" was used to name a group of asteroids which share the Jupiter's orbit around the Sun. The center of mass of the Trojan asteroids is steady relative to Jupiter, once they are trapped on stable Lagrange regions (L 4 and L 5 ) of this celestial mechanical system [1]. In the quantum-mechanical context, Trojan wave packets have non-spreading and nonstationary behavior and they have been observed as a localized Rydberg electron over a circular orbit with dispersion suppressed by external fields [2,3].Quantum walks are the quantum analogue of the classical random walks [4]. The quantum walker is a spin-1/2 particle positioned over discrete positions in a one-dimensional lattice. The quantum walk state is composed by a tensor product between the internal (spin) and external (position) degrees of freedom. The time