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...

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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
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description 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.
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subjects Conditional Mutual Information
Physics
Quantum Markov Chains
Quantum Physics
Recoverability
Strong Subadditivity
title Universal recovery map for approximate Markov chains
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