  We show how entanglement shared between encoder and decoder can simplify the
theory of quantum error correction. The entanglement-assisted quantum codes we
describe do not require the dual-containing constraint necessary for standard
quantum error correcting codes, thus allowing us to ``quantize'' all of
classical linear coding theory. In particular, efficient modern classical codes
that attain the Shannon capacity can be made into entanglement-assisted quantum
codes attaining the hashing bound (closely related to the quantum capacity).
For systems without large amounts of shared entanglement, these codes can also
be used as catalytic codes, in which a small amount of initial entanglement
enables quantum communication.
