  We discuss the capacity of quantum channels for information transmission and
storage. Quantum channels have dual uses: they can be used to transmit known
quantum states which code for classical information, and they can be used in a
purely quantum manner, for transmitting or storing quantum entanglement. We
propose here a definition of the von Neumann capacity of quantum channels,
which is a quantum mechanical extension of the Shannon capacity and reverts to
it in the classical limit. As such, the von Neumann capacity assumes the role
of a classical or quantum capacity depending on the usage of the channel. In
analogy to the classical construction, this capacity is defined as the maximum
von Neumann mutual entropy processed by the channel, a measure which reduces to
the capacity for classical information transmission through quantum channels
(the "Kholevo capacity") when known quantum states are sent. The quantum mutual
entropy fulfills all basic requirements for a measure of information, and
observes quantum data-processing inequalities. We also derive a quantum Fano
inequality relating the quantum loss of the channel to the fidelity of the
quantum code. The quantities introduced are calculated explicitly for the
quantum "depolarizing" channel. The von Neumann capacity is interpreted within
the context of superdense coding, and an "extended" Hamming bound is derived
that is consistent with that capacity.
