  We address decoherence and classicalization of continuous-time quantum walks
(CTQWs) on graphs. In particular, we investigate three different models of
decoherence, and employ the quantum-classical (QC) dynamical distance as a
figure of merit to assess whether, and to which extent, decoherence
classicalizes the CTQW, i.e. turns it into the analogue classical process. We
show that the dynamics arising from intrinsic decoherence, i.e. dephasing in
the energy basis, do not fully classicalize the walker and partially preserves
quantum features. On the other hand, dephasing in the position basis, as
described by the Haken-Strobl master equation or by the quantum stochastic walk
(QSW) model, asymptotically destroys the quantumness of the walker, making it
equivalent to a classical random walk. We also investigate the speed of the
classicalization process, and observe a faster convergence of the QC-distance
to its asymptotic value for intrinsic decoherence and the QSW models, whereas
in the Haken-Strobl scenario, larger values of the decoherence rate induce
localization of the walker.
