  In this work, we investigate the parameters governing the rate at which a
quantum channel arises at the onset of an interaction between two systems, $A$
and $B$. In particular, when system $A$ is pre-entangled with an ancilla,
$\tilde{A}$, we quantify the early-time transmission of pre-existing
entanglement by calculating the leading order change in coherent information of
the complementary channel ($A\rightarrow B'$). We show that, when $A$ and $B$
are initially unentangled and $B$ is pure, there is no change in coherent
information to first order, while the leading (second) order change is
divergent. However, this divergence may be regulated by embedding the
conventional notion of coherent information into what we call the family of
$n$-coherent informations, defined using $n$-R\'enyi entropies. We find that
the rate of change of the $n$-coherent information at the onset of the
interaction is governed by a quantity, which we call the $n$-exposure, which
captures the extent to which the initial coherent information of $A$ with
$\tilde{A}$ is exposed to or `seen by' the interaction Hamiltonian between $A$
and $B$. We give examples in qubit systems and in the light-matter interaction.
