  Entanglement shared between the two ends of a quantum communication channel
has been shown to be a useful resource in increasing both the quantum and
classical capacities for these channels. The entanglement-assisted capacities
were derived assuming an unlimited amount of shared entanglement per channel
use. In this paper, bounds are derived on the minimum amount of entanglement
required per use of a channel, in order to asymptotically achieve the capacity.
This is achieved by introducing a class of entanglement-assisted quantum codes.
Codes for classes of qubit channels are shown to achieve the quantum
entanglement-assisted channel capacity when an amount of shared entanglement
per channel given by, E = 1 - Q_E, is provided. It is also shown that for very
noisy channels, as the capacities become small, the amount of required
entanglement converges for the classical and quantum capacities.

Quantum Physics