Tomamichel, Marco and Berta, Mario and Renes, Joseph M. (2016) Quantum coding with finite resources. Nature Communications, 7 . Art. No. 11419. ISSN 2041-1723. PMCID PMC4865765. doi:10.1038/ncomms11419. https://resolver.caltech.edu/CaltechAUTHORS:20160523-082743757
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Abstract
The quantum capacity of a memoryless channel determines the maximal rate at which we can communicate reliably over asymptotically many uses of the channel. Here we illustrate that this asymptotic characterization is insufficient in practical scenarios where decoherence severely limits our ability to manipulate large quantum systems in the encoder and decoder. In practical settings, we should instead focus on the optimal trade-off between three parameters: the rate of the code, the size of the quantum devices at the encoder and decoder, and the fidelity of the transmission. We find approximate and exact characterizations of this trade-off for various channels of interest, including dephasing, depolarizing and erasure channels. In each case, the trade-off is parameterized by the capacity and a second channel parameter, the quantum channel dispersion. In the process, we develop several bounds that are valid for general quantum channels and can be computed for small instances.
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| Additional Information: | © 2016 Macmillan Publishers Limited. This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ Received 05 August 2015; Accepted 16 March 2016; Published 09 May 2016. We thank Chris Ferrie, Chris Granade, William Matthews, David Sutter and Mark Wilde for helpful discussions. M.T. is funded by an ARC Discovery Early Career Researcher Award Fellowship and acknowledges support from the ARC Centre of Excellence for Engineered Quantum Systems (EQUS). M.B. acknowledges funding provided by the Institute for Quantum Information and Matter. J.M.R. was supported by the Swiss National Science Foundation (through the National Centre of Competence in Research ‘Quantum Science and Technology’). Author contributions: M.T., M.B. and J.R. developed the main ideas and technical results. M.T. wrote the manuscript with the help of M.B. and J.R. The authors declare no competing financial interests. | |||||||||
| Group: | Institute for Quantum Information and Matter | |||||||||
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| PubMed Central ID: | PMC4865765 | |||||||||
| DOI: | 10.1038/ncomms11419 | |||||||||
| Record Number: | CaltechAUTHORS:20160523-082743757 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20160523-082743757 | |||||||||
| Official Citation: | Tomamichel, M. et al. Quantum coding with finite resources. Nat. Commun. 7:11419 doi: 10.1038/ncomms11419 (2016). | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 67248 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 23 May 2016 18:54 | |||||||||
| Last Modified: | 27 Apr 2022 23:12 |
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