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Description
Understanding what makes a quantum process genuinely nonclassical in time is a central question in the foundations of quantum theory. We investigate this question in continuous-time quantum walks by comparing two operational notions of quantumness: a single-time measure based on the quantum–classical dynamical distance, and a multi-time quantifier based on violations of Kolmogorov consistency conditions for sequential measurements. We show that these notions are not equivalent: a quantum walk can reproduce the single-time probability distribution of a classical random walk while still exhibiting genuinely nonclassical temporal correlations. We further show that multi-time nonclassicality displays a universal short-time behavior determined by local connectivity, while at longer times it depends strongly on graph topology. Finally, we analyze the impact of decoherence in different bases, showing that distinct noise mechanisms affect temporal nonclassicality in qualitatively different ways. These results highlight continuous-time quantum walks as a natural setting in which to investigate the temporal structure of quantum processes.