Relative entropy for von Neumann subalgebras

Li Gao, Marius Junge, Nicholas Laracuente

Research output: Contribution to journalArticlepeer-review


We revisit the connection between index and relative entropy for an inclusion of finite von Neumann algebras. We observe that the Pimsner-Popa index connects to sandwiched p-Rényi relative entropy for all 1/2 ≤ p ≤∞, including Umegaki's relative entropy at p = 1. Based on that, we introduce a new notation of relative entropy to a subalgebra which generalizes subfactors index. This relative entropy has application in estimating decoherence time of quantum Markov semigroups.

Original languageEnglish (US)
Article number20500469
JournalInternational Journal of Mathematics
Issue number6
StatePublished - Jun 15 2020


  • Relative entropy
  • subfactor index
  • von Neumann subalgebra

ASJC Scopus subject areas

  • General Mathematics


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