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Entanglement Cost of Quantum Channels

Berta, Mario and Brandão, Fernando G. S. L. and Christandl, Matthias and Wehner, Stephanie (2013) Entanglement Cost of Quantum Channels. IEEE Transactions on Information Theory, 59 (10). pp. 6779-6795. ISSN 0018-9448. doi:10.1109/TIT.2013.2268533.

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The entanglement cost of a quantum channel is the minimal rate at which entanglement (between sender and receiver) is needed in order to simulate many copies of a quantum channel in the presence of free classical communication. In this paper, we show how to express this quantity as a regularized optimization of the entanglement formation over states that can be generated between sender and receiver. Our formula is the channel analog of a well-known formula for the entanglement cost of quantum states in terms of the entanglement of formation and shares a similar relation to the recently shattered hope for additivity. The entanglement cost of a quantum channel can be seen as the analog of the quantum reverse Shannon theorem in the case where free classical communication is allowed. The techniques used in the proof of our result are then also inspired by a recent proof of the quantum reverse Shannon theorem and feature the one-shot formalism for quantum information theory, the postselection technique for quantum channels as well as Sion's minimax theorem. We discuss two applications of our result. First, we are able to link the security in the noisy-storage model to a problem of sending quantum rather than classical information through the adversary's storage device. This not only improves the range of parameters where security can be shown, but also allows us to prove security for storage devices for which no results were known before. Second, our result has consequences for the study of the strong converse quantum capacity. Here, we show that any coding scheme that sends quantum information through a quantum channel at a rate larger than the entanglement cost of the channel has an exponentially small fidelity.

Item Type:Article
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URLURL TypeDescription DOIArticle Paper
Berta, Mario0000-0002-0428-3429
Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:© 2013 IEEE. Manuscript received March 23, 2012; revised December 22, 2012; accepted April 06, 2013. Date of publication July 10, 2013; date of current version September 11, 2013. M. Berta, F. G. S. L. Brandão, and M. Christandl were supported in part by the German Science Foundation under Grant CH 843/2-1, in part by the Swiss National Science Foundation under Grants PP00P2 128455, 20CH21 138799 (CHIST-ERA project CQC), in part by the Swiss National Center of Competence in Research “Quantum Science and Technology (QSIT),” and in part by the Swiss State Secretariat for Education and Research supporting COST action MP1006. F. G. S. L. Brandão was also supported by an EPSRC Early Career fellowship. S. Wehner was supported by the National Research Foundation and Ministry of Education, Singapore and MOE Tier 3 Grant MOE2012-T3-1-009. This paper was presented in part at the 2012 IEEE International Symposium on Information Theory. We acknowledge discussions with J. Oppenheim, M. Walter, R. Werner, M. Wilde, and A. Winter. M. Berta, F. G. S. L. Brandão, and S. Wehner would like to thank the Institute Mittag-Leffler (Djursholm, Sweden), where part of this work was done.
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)CH 843/2-1
Swiss National Science Foundation (SNSF)PP00P2 128455
Swiss National Science Foundation (SNSF)20CH21 138799
Swiss National Center of Competence in ResearchUNSPECIFIED
Swiss State Secretariat for Education and ResearchMP1006
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Ministry of Education (Singapore)MOE2012-T3-1-009
Subject Keywords:Noisy-storage model, quantum channel simulations, quantum cryptography, quantum Shannon theory, strong converse quantum capacity
Issue or Number:10
Record Number:CaltechAUTHORS:20160525-153515356
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Official Citation:M. Berta, F. G. S. L. Brandão, M. Christandl and S. Wehner, "Entanglement Cost of Quantum Channels," in IEEE Transactions on Information Theory, vol. 59, no. 10, pp. 6779-6795, Oct. 2013. doi: 10.1109/TIT.2013.2268533
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:67367
Deposited By: Tony Diaz
Deposited On:26 May 2016 19:29
Last Modified:11 Nov 2021 00:31

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