Universal recovery map for approximate Markov chains
- Creators
- Sutter, David
- Fawzi, Omar
- Renner, Renato
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.
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.Attached Files
Published - 20150623.full.pdf
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Additional details
- Eprint ID
- 68788
- Resolver ID
- CaltechAUTHORS:20160630-133030578
- 258932
- European Research Council (ERC)
- Swiss National Science Foundation (SNSF)
- European Commission
- Created
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2016-07-06Created from EPrint's datestamp field
- Updated
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2021-11-11Created from EPrint's last_modified field