  A general attenuator $\Phi_{\lambda, \sigma}$ is a bosonic quantum channel
that acts by combining the input with a fixed environment state $\sigma$ in a
beam splitter of transmissivity $\lambda$. If $\sigma$ is a thermal state the
resulting channel is a thermal attenuator, whose quantum capacity vanishes for
$\lambda\leq 1/2$. We study the quantum capacity of these objects for generic
$\sigma$, proving a number of unexpected results. Most notably, we show that
for any arbitrary value of $\lambda>0$ there exists a suitable single-mode
state $\sigma(\lambda)$ such that the quantum capacity of
$\Phi_{\lambda,\sigma(\lambda)}$ is larger than a universal constant $c>0$. Our
result holds even when we fix an energy constraint at the input of the channel,
and implies that quantum communication at a constant rate is possible even in
the limit of arbitrarily low transmissivity, provided that the environment
state is appropriately controlled. We also find examples of states $\sigma$
such that the quantum capacity of $\Phi_{\lambda,\sigma}$ is not monotonic in
$\lambda$. These findings may have implications for the study of communication
lines running across integrated optical circuits, of which general attenuators
provide natural models.
