  We consider the problem of transmitting classical and quantum information
reliably over an entanglement-assisted quantum channel. Our main result is a
capacity theorem that gives a three-dimensional achievable rate region. Points
in the region are rate triples, consisting of the classical communication rate,
the quantum communication rate, and the entanglement consumption rate of a
particular coding scheme. The crucial protocol in achieving the boundary points
of the capacity region is a protocol that we name the classically-enhanced
father protocol. The classically-enhanced father protocol is more general than
other protocols in the family tree of quantum Shannon theoretic protocols, in
the sense that several previously known quantum protocols are now child
protocols of it. The classically-enhanced father protocol also shows an
improvement over a time-sharing strategy for the case of a qubit dephasing
channel--this result justifies the need for simultaneous coding of classical
and quantum information over an entanglement-assisted quantum channel. Our
capacity theorem is of a multi-letter nature (requiring a limit over many uses
of the channel), but it reduces to a single-letter characterization for at
least three channels: the completely depolarizing channel, the quantum erasure
channel, and the qubit dephasing channel.
