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Lower Bounds on the Quantum Capacity and Error Exponent of General Memoryless Channels

Tradeoffs between the information rate and fidelity of quantum error-correcting codes are discussed. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a general completely positive linear map, where the dimension of the underlying Hilbert space is a prime number. On such a quantum channel, the highest fidelity of a quantum error-correcting code of length n and rate R is proven to be lower bounded by 1− exp[−nE(R)] for some function E(R). The E(R) is positive below some threshold, which is therefore a lower bound on the quantum capacity.