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The qubit depolarizing channel with noise parameter $\eta$ transmits an inputqubit perfectly with probability $1-\eta$, and outputs the completely mixedstate with probability $\eta$. We show that its complementary channel haspositive quantum capacity for all $\eta>0$. Thus, we find that there exists asingle parameter family of channels having the peculiar property of havingpositive quantum capacity even when the outputs of these channels approach afixed state independent of the input. Comparisons with other related channels,and implications on the difficulty of studying the quantum capacity of thedepolarizing channel are discussed.

On the complementary quantum capacity of the depolarizing channel