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. doi:10.1109/TIT.2018.2873764. https://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.
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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 | ||||||||||||||||||||||||||||
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Subject Keywords: | Communication channels, Channel capacity, Error correction codes, Quantum entanglement, Optimization | ||||||||||||||||||||||||||||
Issue or Number: | 4 | ||||||||||||||||||||||||||||
DOI: | 10.1109/TIT.2018.2873764 | ||||||||||||||||||||||||||||
Record Number: | CaltechAUTHORS:20181011-133942418 | ||||||||||||||||||||||||||||
Persistent URL: | https://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: | 16 Nov 2021 03:30 |
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