  The highest fidelity of quantum error-correcting codes of length n and rate R
is proven to be lower bounded by 1 - exp [-n E(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', which implies R' 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 (e-Print
quant-ph/0109114, LANL, 2001), and M. Hamada, submitted to IEEE Trans. Inf.
Theory, 2002 (e-Print 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 paper to those in the previous works are similar
to that of Markov chains to sequences of independent identically distributed
random variables.
