Approximate Recovery and Relative Entropy I: General von Neumann Subalgebras

Thomas Faulkner, Stefan Hollands, Brian Swingle, Yixu Wang

Research output: Contribution to journalArticlepeer-review


We prove the existence of a universal recovery channel that approximately recovers states on a von Neumann subalgebra when the change in relative entropy, with respect to a fixed reference state, is small. Our result is a generalization of previous results that applied to type-I von Neumann algebras by Junge at al. [arXiv:1509.07127]. We broadly follow their proof strategy but consider here arbitrary von Neumann algebras, where qualitatively new issues arise. Our results hinge on the construction of certain analytic vectors and computations/estimations of their Araki–Masuda Lp norms. We comment on applications to the quantum null energy condition.

Original languageEnglish (US)
Pages (from-to)349-397
Number of pages49
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - Jan 2022

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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