  Entanglement-assisted concatenated quantum codes (EACQCs), constructed by
concatenating two quantum codes, are proposed. These EACQCs show several
advantages over the standard concatenated quantum codes (CQCs). Several
families of EACQCs that, unlike standard CQCs, can beat the nondegenerate
Hamming bound for entanglement-assisted quantum error correction codes
(EAQECCs) are derived. Further, a number of EACQCs with better parameters than
the best known standard quantum error correction codes (QECCs) and EAQECCs are
also derived. In particular, several catalytic EACQCs with better parameters
than the best known QECCs of the same length and net transmission are
constructed. Furthermore, each catalytic EACQC consumes only one or two ebits.
It is also shown that EACQCs make entanglement-assisted quantum communication
possible even if the ebits are noisy. Finally, it is shown that EACQCs can
outperform CQCs in entanglement fidelity over depolarizing channels if the
ebits are less noisy than the qubits. Moreover, the threshold error probability
of EACQCs is larger than that of CQCs when the error probability of ebits is
sufficiently lower than that of qubits. Therefore EACQCs are not only
competitive in quantum communication but also applicable in fault-tolerant
quantum computation.
