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Conditional Decoupling of Quantum Information

Berta, Mario and Brandão, Fernando G. S. L. and Majenz, Christian and Wilde, Mark M. (2018) Conditional Decoupling of Quantum Information. Physical Review Letters, 121 (4). Art. No. 040504. ISSN 0031-9007. http://resolver.caltech.edu/CaltechAUTHORS:20180727-091530188

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Abstract

Insights from quantum information theory show that correlation measures based on quantum entropy are fundamental tools that reveal the entanglement structure of multipartite states. In that spirit, Groisman, Popescu, and Winter [Phys. Rev. A 72, 032317 (2005)] showed that the quantum mutual information I(A;B) quantifies the minimal rate of noise needed to erase the correlations in a bipartite state of quantum systems AB. Here, we investigate correlations in tripartite systems ABE. In particular, we are interested in the minimal rate of noise needed to apply to the systems AE in order to erase the correlations between A and B given the information in system E, in such a way that there is only negligible disturbance on the marginal BE. We present two such models of conditional decoupling, called deconstruction and conditional erasure cost of tripartite states ABE. Our main result is that both are equal to the conditional quantum mutual information I(A;B|E)—establishing it as an operational measure for tripartite quantum correlations.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/physrevlett.121.040504DOIArticle
https://arxiv.org/abs/1808.00135arXivDiscussion Paper
ORCID:
AuthorORCID
Berta, Mario0000-0002-0428-3429
Brandão, Fernando G. S. L.0000-0003-3866-9378
Wilde, Mark M.0000-0002-3916-4462
Additional Information:© 2018 American Physical Society. (Received 7 February 2017; revised manuscript received 9 January 2018; published 27 July 2018) We are indebted to G. Gour, M. Hastings, M. Piani, S. Das, M. Murao, K. Seshadreesan, E. Wakakuwa, and A. Winter for valuable discussions. We acknowledge the catalyzing role of the open problems session at Beyond IID, which ultimately led to the results presented here. C. M. acknowledges financial support from the European Research Council (ERC Grant Agreement No. 337603), the Danish Council for Independent Research (Sapere Aude) and VILLUM FONDEN via the QMATH Centre of Excellence (Grant No. 10059). M. M. W. acknowledges support from the NSF under Grant No. 1714215.
Group:Institute for Quantum Information and Matter, IQIM
Funders:
Funding AgencyGrant Number
European Research Council (ERC)337603
Danish Council for Independent ResearchUNSPECIFIED
Villum Fonden10059
NSFCCF-1714215
Issue or Number:4
Record Number:CaltechAUTHORS:20180727-091530188
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180727-091530188
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88320
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:30 Jul 2018 14:31
Last Modified:01 Aug 2019 20:21

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