2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/91837We 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.9 pages, to appear in the Festschrift celebrating Alexander S. Holevo's 60'th birthdayQuantum Physicstext