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When a noisy communication channel is used multiple times, the errors occurring at different times generally exhibit correlations. Classically, these correlations do not affect the evolution of individual particles: a single classical particle can only traverse the channel at a definite moment of time, and its evolution is insensitive to the correlations between subsequent uses of the channel. In stark contrast, here we show that a single quantum particle can sense the correlations between multiple uses of a channel at different moments of time. In an extreme example, we show that a channel that outputs white noise when the particle is sent at a definite time can exhibit correlations that enable a perfect transmission of classical bits when the particle is sent at a superposition of two times. In contrast, we show that, in the lack of correlations, a single particle sent at a superposition of two times undergoes an effective channel with classical capacity of at most 0.16 bits. When multiple transmission lines are available, time correlations can be used to simulate the application of quantum channels in a coherent superposition of alternative causal orders, and even to provide communication advantages that are not accessible through the superposition of causal orders., Comment: 20 pages