On the complementary quantum capacity of the depolarizing channel

Debbie Leung1 and John Watrous2

1Institute for Quantum Computing and Department of Combinatorics and Optimization, University of Waterloo
2Institute for Quantum Computing and School of Computer Science, University of Waterloo

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Updated version: The authors have uploaded version v4 of this work to the arXiv which may contain updates or corrections not contained in the published version v3. The authors left the following comment on the arXiv:
v4 corrects errors in equation (38)


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 $\eta\gt 0$. 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.

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