  We give the trade-off curve showing the capacity of a quantum channel as a
function of the amount of entanglement used by the sender and receiver for
transmitting information. The endpoints of this curve are given by the
Holevo-Schumacher-Westmoreland capacity formula and the entanglement-assisted
capacity, which is the maximum over all input density matrices of the quantum
mutual information. The proof we give is based on the
Holevo-Schumacher-Westmoreland formula, and also gives a new and simpler proof
for the entanglement-assisted capacity formula.
