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Smooth Entropy Bounds on One-Shot Quantum State Redistribution

Berta, Mario and Christandl, Matthias and Touchette, Dave (2016) Smooth Entropy Bounds on One-Shot Quantum State Redistribution. IEEE Transactions on Information Theory, 62 (3). pp. 1425-1439. ISSN 0018-9448. doi:10.1109/TIT.2016.2516006.

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In quantum state redistribution as introduced by Luo and Devetak and Devetak and Yard, there are four systems of interest: the A system held by Alice; the B system held by Bob; the C system that is to be transmitted from Alice to Bob; and the R system that holds a purification of the state in the ABC registers. We give upper and lower bounds on the amount of quantum communication and entanglement required to perform the task of quantum state redistribution in a one-shot setting. Our bounds are in terms of the smooth conditional min- and max-entropy, and the smooth max-information. The protocol for the upper bound has a clear structure, building on the work of Oppenheim: it decomposes the quantum state redistribution task into two simpler coherent state merging tasks by introducing a coherent relay. In the independent and identical (i.i.d.) asymptotic limit our bounds for the quantum communication cost converge to the quantum conditional mutual information I (C; R|B), and our bounds for the total cost converge to the conditional entropy H(C|B). This yields an alternative proof of optimality of these rates for quantum state redistribution in the i.i.d. asymptotic limit. In particular, we obtain a strong converse for quantum state redistribution, which even holds when allowing for feedback.

Item Type:Article
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URLURL TypeDescription Paper
Berta, Mario0000-0002-0428-3429
Additional Information:© 2016 IEEE. Manuscript received September 16, 2015; revised December 22, 2015; accepted December 22, 2015. Date of publication January 8, 2016; date of current version February 12, 2016. M. Berta was supported in part by the Institute for Quantum Information and Matter through the National Science Foundation Physics Frontiers Center Program under Grant PHY-1125565, in part by the Gordon and Betty Moore Foundation under Grant 12500028, and in part by the ARO Grant for Research on Quantum Algorithms through the IQIM Program under Grant W911NF-12-1-0521. M. Christandl was supported in part by a Sapere Aude Grant within the Danish Council for Independent Research, in part by an ERC Starting Grant through the CHIST-ERA Project CQC, in part by an SNSF Professorship, in part by the Swiss NCCR QSIT, and in part by the Swiss SBFI in Relation to COST Action Program under Grant MP1006. D. Touchette was supported in part by the FRQNT B2 Doctoral Research Scholarship Program, in part by CryptoWorks21, in part by NSERC and Industry Canada. The Institute for Quantum Computing and the Perimeter Institute for Theoretical Physics are supported in part by the Government of Canada and the province of Ontario. The authors thank Felix Leditzky for discussions about [22]. These discussions were the starting point for the derivations in Sections V-D and V-E. They acknowledge discussions with Renato Renner, Mark Wilde, and Jürg Wullschleger. The hospitality of the Banff International Research Station (BIRS) during the workshop “Beyond i.i.d. in Information Theory” (July 5–10, 2015) is gratefully acknowledged (the work in Sections V-D and V-E was done there).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore Foundation12500028
Army Research Office (ARO)W911NF-12-1-0521
Danish Council for Independent ResearchUNSPECIFIED
European Research Council (ERC)UNSPECIFIED
Swiss National Science Foundation (SNSF)UNSPECIFIED
Swiss State Secretariat for Education and ResearchMP1006
Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT)UNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Industry CanadaUNSPECIFIED
Government of CanadaUNSPECIFIED
Province of OntarioUNSPECIFIED
Subject Keywords:Quantum mechanics, quantum entanglement, information theory, entropy
Issue or Number:3
Record Number:CaltechAUTHORS:20160216-131540447
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Official Citation:Berta, M.; Christandl, M.; Touchette, D., "Smooth Entropy Bounds on One-Shot Quantum State Redistribution," in Information Theory, IEEE Transactions on , vol.62, no.3, pp.1425-1439, March 2016 doi: 10.1109/TIT.2016.2516006
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64514
Deposited By: Tony Diaz
Deposited On:17 Feb 2016 22:06
Last Modified:10 Nov 2021 23:32

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