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 journalArticlepeer-review


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 (US)
Pages (from-to)2955-2978
Number of pages24
JournalAnnales Henri Poincare
Issue number10
StatePublished - Oct 1 2018

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics


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