Most coding theorems in quantum Shannon theory can be proven using the
decoupling technique: to send data through a channel, one guarantees that the
environment gets no information about it; Uhlmann's theorem then ensures that
the receiver must be able to decode. While a wide range of problems can be
solved this way, one of the most basic coding problems remains impervious to a
direct application of this method: sending classical information through a
quantum channel. We will show that this problem can, in fact, be solved using
decoupling ideas, specifically by proving a "dequantizing" theorem, which
ensures that the environment is only classically correlated with the sent data.
Our techniques naturally yield a generalization of the
Holevo-Schumacher-Westmoreland Theorem to the one-shot scenario, where a
quantum channel can be applied only once
