VON-NEUMANN CAPACITY OF NOISY QUANTUM CHANNELS

We discuss the capacity of quantum channels for information transmissi on and storage. Quantum channels have dual uses: they can be used to t ransmit known quantum states which code for classical information, and they can be used in a purely quantum manner, for transmitting or stor ing quantum entanglement. We propose here a definition of the von Neum ann capacity of quantum channels, which is a quantum-mechanical extens ion 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 q uantum capacity depending on the usage of the channel. In analogy to t he classical construction, this capacity is defined as the maximum von Neumann mutual entropy processed by the channel, a measure which redu ces to the capacity for classical information transmission through qua ntum channels (the ''Kholevo capacity'') when known quantum stares are sent. The quantum mutual entropy fulfills all basic requirements for a measure of information, and observes quantum data-processing inequal ities. We also derive a quantum Fano inequality relating the quantum l oss of the channel to the fidelity of the quantum code. The quantities introduced are calculated explicitly for the quantum depolarizing cha nnel. The von Neumann capacity is interpreted within the context of su perdense coding, and an extended Hamming bound is derived that is cons istent with that capacity. [S1050-2947(97)04511-3].