An exponential lower bound on the highest fidelity achievable by quantum error-correcting codes

On a quantum memoryless 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)+o(n)] for some function E(R). The E(R) is positive below some threshold R₀, a direct consequence of which is that R₀ is a lower bound on the quantum capacity of the channel.