Universal recovery map for approximate Markov chains

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 informat...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2016-02, Vol.472 (2186), p.20150623-20150623
Main Authors: Sutter, David, Fawzi, Omar, Renner, Renato
Format: Article
Language:English
Subjects:
Conditional Mutual Information
Physics
Quantum Markov Chains
Quantum Physics
Recoverability
Strong Subadditivity
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2015.0623