A lower bound on the quantum capacity of channels with correlated errors

The highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1-exp[-nE(R)+o(n)] for some function E(R) on noisy quantum channels that are subject to not necessarily independent errors. The E(R) is positive below some threshold R-0, which implies R-0 is a lower bound on the quantum capacity. This work is an extension of the author's previous works [M. Hamada, Phys. Rev. A, 65, 052305 (2002); quant-ph/0109114, LANL (2001); M. Hamada, quant-ph/0112103, LANL (2001)], which presented the bound for channels subject to independent errors, or channels modeled as tensor products of copies of a completely positive linear map. The relation of the channel class treated in this article to those in the previous works is similar to that of Markov chains to sequences of independent identically distributed random variables. (C) 2002 American Institute of Physics.