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Universal recovery map for approximate Markov chains

Sutter, David and Fawzi, Omar and Renner, Renato (2016) Universal recovery map for approximate Markov chains. Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences, 472 (2186). Art. No. 20150623. ISSN 1364-5021. https://resolver.caltech.edu/CaltechAUTHORS:20160630-133030578

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Abstract

A central question in quantum information theory is to determine how well lost information can be reconstructed. Crucially, the corresponding recovery operation should perform well without knowing the information to be reconstructed. In this work, we show that the quantum conditional mutual information measures the performance of such recovery operations. More precisely, we prove that the conditional mutual information I(A:C|B) of a tripartite quantum state ρABC can be bounded from below by its distance to the closest recovered state RB→BC(ρAB), where the C-part is reconstructed from the B-part only and the recovery map RB→BC merely depends on ρBC. One particular application of this result implies the equivalence between two different approaches to define topological order in quantum systems.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1098/rspa.2015.0623DOIArticle
http://rspa.royalsocietypublishing.org/content/472/2186/20150623PublisherArticle
Additional Information:© 2016 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. Received: 8 September 2015; Accepted: 24 December 2015. Data accessibility. This work does not have any experimental data. Authors’ contributions. All authors contributed equally to this work. Competing interests. We have no competing interests. Funding. This project was supported by the European Research Council (ERC) via grant no. 258932, by the Swiss National Science Foundation (SNSF) via the National Centre of Competence in Research ‘QSIT’, and by the European Commission via the project ‘RAQUEL’. We thank Mario Berta, Fernando Brandão, Philipp Kammerlander, Joseph Renes, Volkher Scholz, Marco Tomamichel and MarkWilde for discussions about approximate Markov chains.
Funders:
Funding AgencyGrant Number
European Research Council (ERC)258932
Swiss National Science Foundation (SNSF)UNSPECIFIED
European CommissionUNSPECIFIED
Subject Keywords:conditional mutual information, quantum Markov chains, recoverability, strong subadditivity
Issue or Number:2186
Record Number:CaltechAUTHORS:20160630-133030578
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160630-133030578
Official Citation:Universal recovery map for approximate Markov chains David Sutter, Omar Fawzi, Renato Renner Proc. R. Soc. A 2016 472 20150623; DOI: 10.1098/rspa.2015.0623. Published 3 February 2016
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:68788
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:06 Jul 2016 02:28
Last Modified:03 Oct 2019 10:16

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