Relative entropy for von Neumann subalgebras

Li Gao, Marius Junge, Nicholas Laracuente

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume31
Issue number6
DOIs
StatePublished - Jun 15 2020

Keywords

  • Relative entropy
  • subfactor index
  • von Neumann subalgebra

ASJC Scopus subject areas

  • Mathematics(all)

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