On the complementary quantum capacity of the depolarizing channel

TL;DR

This paper proves that the complementary channel of the qubit depolarizing channel always has positive quantum capacity for any non-zero noise level, revealing a surprising property of quantum information transmission.

Contribution

It demonstrates that the complementary channel of the depolarizing channel maintains positive quantum capacity for all positive noise parameters, a novel insight into quantum channel behavior.

Findings

Complementary depolarizing channels have positive quantum capacity for all $\, ext{eta}>0$.

The output of these channels approaches a fixed state regardless of input.

Implications for understanding quantum capacity of noisy channels.

Abstract

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