Quantum and Private Capacities of Low-Noise Channels

Felix Leditzky, Debbie Leung, Graeme Smith

Research output: Contribution to journalArticlepeer-review


We determine both the quantum and the private capacities of low-noise quantum channels to leading orders in the channel's distance to the perfect channel. It has been an open problem for more than 20 yr to determine the capacities of some of these low-noise channels such as the depolarizing channel. We also show that both capacities are equal to the single-letter coherent information of the channel, again to leading orders. We thus find that, in the low-noise regime, superadditivity and degenerate codes have a negligible benefit for the quantum capacity, and shielding does not improve the private capacity beyond the quantum capacity, in stark contrast to the situation when noisier channels are considered.

Original languageEnglish (US)
Article number160503
JournalPhysical review letters
Issue number16
StatePublished - Apr 20 2018
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy


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