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Quantum capacity bounds of Gaussian thermal loss channels and achievable rates with Gottesman-Kitaev-Preskill codes

Noh, Kyungjoo and Albert, Victor V. and Jiang, Liang (2019) Quantum capacity bounds of Gaussian thermal loss channels and achievable rates with Gottesman-Kitaev-Preskill codes. IEEE Transactions on Information Theory, 65 (4). pp. 2563-2582. ISSN 0018-9448. http://resolver.caltech.edu/CaltechAUTHORS:20181011-133942418

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Abstract

Gaussian thermal loss channels are of particular importance to quantum communication theory since they model realistic optical communication channels. Except for special cases, the quantum capacity of Gaussian thermal loss channels is not yet quantified completely. In this paper, we provide improved upper bounds of the Gaussian thermal loss channel capacity, both in energy-constrained and unconstrained scenarios. We briefly review Gottesman-Kitaev-Preskill (GKP) codes and discuss their experimental implementation. We then prove, in the energyunconstrained case, that a family of GKP codes achieves the quantum capacity of Gaussian thermal loss channels up to at most a constant gap from the improved upper bound. In the energy-constrained case, we formulate a biconvex encoding and decoding optimization problem to maximize entanglement fidelity. Then, we solve the biconvex optimization heuristically by an alternating semidefinite programming (SDP) method and report that, starting from Haar random initial codes, our numerical optimization yields a hexagonal GKP code as an optimal encoding in a practically relevant regime.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/TIT.2018.2873764DOIArticle
https://arxiv.org/abs/1801.07271arXivDiscussion Paper
ORCID:
AuthorORCID
Noh, Kyungjoo0000-0002-6318-8472
Albert, Victor V.0000-0002-0335-9508
Jiang, Liang0000-0002-0000-9342
Alternate Title:Improved quantum capacity bounds of Gaussian loss channels and achievable rates with Gottesman-Kitaev-Preskill codes
Additional Information:© 2018 IEEE. Manuscript received February 7, 2018; revised July 7, 2018 and September 23, 2018; accepted September 24, 2018. Date of publication October 5, 2018; date of current version March 15, 2019. We would like to thank Steven M. Girvin, Barbara Terhal, John Preskill, Steven T. Flammia, Sekhar Tatikonda, Richard Kueng, Linshu Li and Mengzhen Zhang for fruitful discussions. We also thank Mark M. Wilde and Matteo Rosati for useful comments on our manuscript. We acknowledge support from the ARL-CDQI (W911NF-15-2-0067), ARO (W911NF-14-1-0011, W911NF-14-1-0563, W911NF-18-1-0020, W911NF-18-1-0212), ARO MURI (W911NF-16-1-0349), AFOSR MURI (FA9550-14-1-0052, FA9550-15-1-0015), NSF (EFMA-1640959), the Alfred P. Sloan Foundation (BR2013-049), and the Packard Foundation (2013-39273). KN acknowledges support through the Korea Foundation for Advanced Studies. VAA acknowledges support from the Walter Burke Institute for Theoretical Physics at Caltech.
Group:Walter Burke Institute for Theoretical Physics, Institute for Quantum Information and Matter, IQIM
Funders:
Funding AgencyGrant Number
Army Research Office (ARO)W911NF-15-2-0067
Army Research Office (ARO)W911NF-14-1-0011
Army Research Office (ARO)W911NF-14-1-0563
Army Research Office (ARO)W911NF-18-1-0020
Army Research Office (ARO)W911NF-18-1-0212
Army Research Office (ARO)W911NF-16-1-0349
Air Force Office of Scientific Research (AFOSR)FA9550-14-1-0052
Air Force Office of Scientific Research (AFOSR)FA9550-15-1-0015
NSFEFMA-1640959
Alfred P. Sloan FoundationBR2013-049
David and Lucile Packard Foundation2013-39273
Korea Foundation for Advanced StudiesUNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Subject Keywords:Communication channels, Channel capacity, Error correction codes, Quantum entanglement, Optimization
Record Number:CaltechAUTHORS:20181011-133942418
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20181011-133942418
Official Citation:K. Noh, V. V. Albert and L. Jiang, "Quantum Capacity Bounds of Gaussian Thermal Loss Channels and Achievable Rates With Gottesman-Kitaev-Preskill Codes," in IEEE Transactions on Information Theory, vol. 65, no. 4, pp. 2563-2582, April 2019. doi: 10.1109/TIT.2018.2873764
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90253
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:12 Oct 2018 12:32
Last Modified:20 Mar 2019 17:18

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