  Prior entanglement between sender and receiver, which exactly doubles the
classical capacity of a noiseless quantum channel, can increase the classical
capacity of some noisy quantum channels by an arbitrarily large constant factor
depending on the channel, relative to the best known classical capacity
achievable without entanglement. The enhancement factor is greatest for very
noisy channels, with positive classical capacity but zero quantum capacity.
Although such quantum channels can be simulated classically, no violation of
causality is implied, because the simulation requires at least as much forward
classical communication as the entanglement-assisted classical capacity of the
channel being simulated. We obtain exact expressions for the
entanglement-assisted capacity of depolarizing and erasure channels in d
dimensions.
