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Converse Bounds for Private Communication Over Quantum Channels

Wilde, Mark M. and Tomamichel, Marco and Berta, Mario (2017) Converse Bounds for Private Communication Over Quantum Channels. IEEE Transactions on Information Theory, 63 (3). pp. 1792-1817. ISSN 0018-9448. https://resolver.caltech.edu/CaltechAUTHORS:20170221-082750394

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Abstract

This paper establishes several converse bounds on the private transmission capabilities of a quantum channel. The main conceptual development builds firmly on the notion of a private state, which is a powerful, uniquely quantum method for simplifying the tripartite picture of privacy involving local operations and public classical communication to a bipartite picture of quantum privacy involving local operations and classical communication. This approach has previously led to some of the strongest upper bounds on secret key rates, including the squashed entanglement and the relative entropy of entanglement. Here, we use this approach along with a “privacy test” to establish a general meta-converse bound for private communication, which has a number of applications. The meta-converse allows for proving that any quantum channel’s relative entropy of entanglement is a strong converse rate for private communication. For covariant channels, the meta-converse also leads to second-order expansions of relative entropy of entanglement bounds for private communication rates. For such channels, the bounds also apply to the private communication setting in which the sender and the receiver are assisted by unlimited public classical communication, and as such, they are relevant for establishing various converse bounds for quantum key distribution protocols conducted over these channels. We find precise characterizations for several channels of interest and apply the methods to establish converse bounds on the private transmission capabilities of all phase-insensitive bosonic channels.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/TIT.2017.2648825DOIArticle
http://ieeexplore.ieee.org/document/7807212/PublisherArticle
https://arxiv.org/abs/1602.08898arXivDiscussion Paper
ORCID:
AuthorORCID
Tomamichel, Marco0000-0001-5410-3329
Berta, Mario0000-0002-0428-3429
Additional Information:© 2017 IEEE. Manuscript received September 7, 2016; accepted December 26, 2016. Date of publication January 5, 2017; date of current version February 14, 2017. This work was supported by the ARO grant for Research on Quantum Algorithms at the IQIM under Grant W911NF-12-1-0521. M. M. Wilde was supported in part by the NSF under Award CCF-1350397 and in part by the Office of Naval Research. M. Tomamichel was supported in part by the University of Sydney Postdoctoral Fellowship and in part by the ARC Centre of Excellence for Engineered Quantum Systems. M. Berta was supported in part by the Institute for Quantum Information and Matter, in part by the NSF Physics Frontiers Center NFS under Grant PHY-1125565, and in part by the Gordon and Betty Moore Foundation under Grant GBMF-12500028. The authors are grateful to Siddhartha Das, Nilanjana Datta, Eleni Diamanti, Kenneth Goodenough, Michal Horodecki, Felix Leditzky, Will Matthews, Alexander Müller-Hermes, Yan Pautrat, Stefano Pirandola, Joe Renes, David Sutter, Masahiro Takeoka, and Stephanie Wehner for helpful discussions. Marco Tomamichel and Mario Berta thank the Hearne Institute for Theoretical Physics at Louisiana State University for hosting them for a research visit in March 2016.
Group:Institute for Quantum Information and Matter, IQIM
Funders:
Funding AgencyGrant Number
Army Research Office (ARO)W911NF-12-1-0521
NSFCCF-1350397
Office of Naval Research (ONR)UNSPECIFIED
University of SydneyUNSPECIFIED
Australian Research CouncilUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterPHY-1125565
Gordon and Betty Moore FoundationGBMF-12500028
Subject Keywords:Bipartite private state, tripartite key state, meta-converse, relative entropy of entanglement, secret key transmission, privacy test, phase-insensitive bosonic Gaussian channel
Issue or Number:3
Record Number:CaltechAUTHORS:20170221-082750394
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170221-082750394
Official Citation:M. M. Wilde, M. Tomamichel and M. Berta, "Converse Bounds for Private Communication Over Quantum Channels," in IEEE Transactions on Information Theory, vol. 63, no. 3, pp. 1792-1817, March 2017. doi: 10.1109/TIT.2017.2648825
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74419
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:21 Feb 2017 17:32
Last Modified:03 Oct 2019 16:38

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