  We consider situations in which i) Alice wishes to send quantum information
to Bob via a noisy quantum channel, ii) Alice has a classical description of
the states she wishes to send and iii) Alice can make use of a finite amount of
noiseless classical information. After setting up the problem in general, we
focus attention on one specific scenario in which Alice sends a known qubit
down a depolarizing channel along with a noiseless cbit. We describe a protocol
which we conjecture is optimal and calculate the average fidelity obtained. A
surprising amount of structure is revealed even for this simple case which
suggests that relationships between quantum and classical information could in
general be very intricate.
