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Public Quantum Communication and Superactivation

Brandão, F. G. S. L. and Oppenheim, J. (2013) Public Quantum Communication and Superactivation. IEEE Transactions on Information Theory, 59 (4). pp. 2517-2526. ISSN 0018-9448. doi:10.1109/TIT.2012.2236911.

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Is there a meaningful quantum counterpart to public communication? We argue that it is the symmetric-side channel. This connection is partially motivated by recent work, where it was found that if a sender would like to communicate a secret message to a receiver through an insecure quantum channel using a shared quantum state as a key, then the insecure quantum channel is only ever used to simulate a symmetric-side channel. Here, we further show, in complete analogy to the role of public classical communication, that assistance by a symmetric-side channel makes equal the distillable entanglement, the recently introduced mutual independence, and a generalization of the latter, which quantifies the extent to which one of the parties can perform quantum privacy amplification. Symmetric-side channels, and the closely related erasure channel, have been recently harnessed to provide examples of superactivation of the quantum channel capacity. Our findings give new insight into this nonadditivity and its relation to quantum privacy. In particular, we show that single-copy superactivation protocols with the erasure channel, which encompasses all examples of nonadditivity of the quantum capacity found to date, can be understood as a conversion of mutual independence into distillable entanglement.

Item Type:Article
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URLURL TypeDescription
Brandão, F. G. S. L.0000-0003-3866-9378
Oppenheim, J.0000-0002-8993-412X
Additional Information:© 2013 IEEE. Manuscript received July 21, 2010; revised October 09, 2012; accepted December 19, 2012. Date of publication January 04, 2013; date of current version March 13, 2013. F. G. S. L. Brandão was supported by a “Conhecimento Novo” fellowship from Fundação de Amparo a Pesquisa do Estado de Minas Gerais. J. Oppenheim was supported in part by the Royal Society and in part by the National Science Foundation under grant PHY-0551164, while at Kavli Institute for Theoretical Physics, Santa Barbara. We are grateful to Graeme Smith for interesting discussions, and his helpful comments on an early draft of this work. JO thanks the hospitality of KITP, Santa Barbara during his stay.
Funding AgencyGrant Number
Fundação de Amparo a Pesquisa do Estado de Minas Gerais (FAPEMIG)UNSPECIFIED
Subject Keywords:Mutual independence, privacy, public quantum communication, quantum one-time pad, symmetric-side channels, weak mutual independence
Issue or Number:4
Record Number:CaltechAUTHORS:20160524-093536574
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Official Citation:F. G. S. L. Brandao and J. Oppenheim, "Public Quantum Communication and Superactivation," in IEEE Transactions on Information Theory, vol. 59, no. 4, pp. 2517-2526, April 2013. doi: 10.1109/TIT.2012.2236911
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:67298
Deposited By: Tony Diaz
Deposited On:24 May 2016 16:40
Last Modified:11 Nov 2021 00:30

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