  An expression is derived characterizing the set of admissible rate pairs for
simultaneous transmission of classical and quantum information over a given
quantum channel, generalizing both the classical and quantum capacities of the
channel. Although our formula involves regularization, i.e. taking a limit over
many copies of the channel, it reduces to a single-letter expression in the
case of generalized dephasing channels. Analogous formulae are conjectured for
the simultaneous public-private capacity of a quantum channel and for the
simultaneously 1-way distillable common randomness and entanglement of a
bipartite quantum state.
