Universal Recovery Maps and Approximate Sufficiency of Quantum Relative Entropy

Marius Junge, Renato Renner, David Sutter, Mark M. Wilde, Andreas Winter

Research output: Contribution to journalArticleResearch

40 Citations (Scopus)


© 2018, The Author(s). The data processing inequality states that the quantum relative entropy between two states ρ and σ can never increase by applying the same quantum channel N to both states. This inequality can be strengthened with a remainder term in the form of a distance between ρ and the closest recovered state (R∘ N) (ρ) , where R is a recovery map with the property that σ= (R∘ N) (σ). We show the existence of an explicit recovery map that is universal in the sense that it depends only on σ and the quantum channel N to be reversed. This result gives an alternate, information-theoretic characterization of the conditions for approximate quantum error correction.
Original languageEnglish
Pages (from-to)2955-2978
JournalAnnales Henri Poincare
Publication statusPublished - 1 Oct 2018


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