TY - GEN
T1 - Quantum and private capacities of low-noise channels
AU - Leditzky, Felix
AU - Leung, Debbie
AU - Smith, Graeme
N1 - Funding Information:
V. ACKNOWLEDGEMENTS We thank Charles Bennett, Ke Li, John Smolin, and John Watrous for inspiring discussions. DL is further supported by NSERC and CIFAR, and FL and GS by the National Science Foundation under Grant Number 1125844.
Publisher Copyright:
© 2017 IEEE.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/1/31
Y1 - 2018/1/31
N2 - 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 years 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, super-additivity and degenerate codes have 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.
AB - 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 years 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, super-additivity and degenerate codes have 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.
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U2 - 10.1109/ITW.2017.8278040
DO - 10.1109/ITW.2017.8278040
M3 - Conference contribution
AN - SCOPUS:85046342168
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 484
EP - 488
BT - 2017 IEEE Information Theory Workshop, ITW 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 IEEE Information Theory Workshop, ITW 2017
Y2 - 6 November 2017 through 10 November 2017
ER -