Quantum and Private Capacities of Low-Noise Channels

Physical Review Letters
Felix LeditzkyGraeme Smith

Abstract

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.

References

May 21, 2005·Physical Review Letters·Karol HorodeckiJonathan Oppenheim
Mar 16, 2007·Physical Review Letters·Graeme Smith, John A Smolin
Jun 4, 2008·Physical Review Letters·Graeme SmithJohn A Smolin
Aug 23, 2008·Science·Graeme Smith, Jon Yard
Oct 2, 2009·Physical Review Letters·Ke LiGuangCan Guo
Oct 2, 2009·Physical Review Letters·Graeme Smith, John A Smolin
Aug 2, 2014·Physical Review Letters·Debbie LeungJohn A Smolin
Apr 1, 2015·Nature Communications·Toby CubittSergii Strelchuk
Feb 12, 2017·Physical Review Letters·Andrew CrossGraeme Smith

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Citations

Sep 7, 2019·Physical Review Letters·Eneet KaurAndreas Winter
Nov 6, 2018·Physical Review Letters·Felix LeditzkyGraeme Smith
Jul 24, 2020·Physical Review Letters·Marco FanizzaVittorio Giovannetti
Oct 3, 2021·Nature Communications·Vikesh Siddhu

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