  Communication between a free-falling observer and an observer hovering above
the Schwarzschild horizon of a black hole suffers from Unruh-Hawking noise,
which degrades communication channels. Ignoring time dilation, which affects
all channels equally, we show that for bosonic communication using single and
dual rail encoding the classical channel capacity reaches a finite value and
the quantum coherent information tends to zero. We conclude that classical
correlations still exist at infinite acceleration, whereas the quantum
coherence is fully removed.
