  In a recent work (Borras et al., Phys. Rev. A {\bf 79}, 022108 (2009)), we
have determined, for various decoherence channels, four-qubit initial states
exhibiting the most robust possible entanglement. Here we explore some
geometrical features of the trajectories in state space generated by the
decoherence process, connecting the initially robust pure state with the
completely decohered mixed state obtained at the end of the evolution. We
characterize these trajectories by recourse to the distance between the
concomitant time dependent mixed state and different reference states.
