On quantum fidelities and channel capacities

For the discrete memoryless quantum channel, me show the equivalence of two different notions of quantum channel capacity: that which uses the entangl ement fidelity as its criterion for success in transmission, and that which uses the minimum fidelity of pure states in a subspace of the input Hilber t space as its criterion. As a corollary, arty source with entropy rate les s than the capacity may be transmitted with high entanglement fidelity. We also show that a restricted class of encodings is sufficient to transmit an y quantum source which may be transmitted on a given channel. This enables us to simplify a known upper bound for the channel capacity It also enables us to show that the availability of an auxiliary classical channel from en coder to decoder does not increase the quantum capacity.