  Single-file transport refers to the motion of particles in a narrow channel,
such that they cannot bypass each other. This constraint leads to strong
correlations between the particles, described by correlation profiles, which
measure the correlation between a generic observable and the density of
particles at a given position and time. They have recently been shown to play a
central role in single-file systems. Up to now, these correlations have only
been determined for diffusive systems in the hydrodynamic limit. Here, we
consider a model of reflecting point particles on the infinite line, with a
general individual stochastic dynamics. We show that the correlation profiles
take a simple universal form, at arbitrary time. We illustrate our approach by
the study of the integrated current of particles through the origin, and apply
our results to representative models such as Brownian particles, run-and-tumble
particles and L\'evy flights. We further emphasise the generality of our
results by showing that they also apply beyond the 1d case, and to other
observables.
