  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.
