The asymptotic probability distribution of the relative distance of additive quantum codes ✩

For given information rate R, it is proved as n tends to infinite, that almost all additive [[n, n · R]] quantum codes (pure and impure) are the codes with their relative distance tending to h−1(1 − R), where h(x)=−x logx/3 2 −(1 − x) log1−x 2 is an entropy function. © 2007 Elsevier Inc. All rights reserved.