Von Neumann entropy and majorization

Paul Busch, Yuan Li

Research output: Contribution to journalArticlepeer-review


We consider the properties of the Shannon entropy for two probability distributions which stand in the relationship of majorization. Then we give a generalization of a theorem due to Uhlmann, extending it to infinite dimensional Hilbert spaces. Finally we show that for any quantum channel Φ, one has S(Φ(ρ)) = S(ρ) for all quantum states ρ if and only if there exists an isometric operator V such that Φ(ρ)=VρV*.
Original languageEnglish
Pages (from-to)384-393
Number of pages10
JournalJournal of mathematical analysis and applications
Issue number1
Early online date15 Jun 2013
Publication statusPublished - 1 Dec 2013

Bibliographical note

© 2013, Elsevier Inc. This is an author produced version of the paper published in Journal of Mathematical Analysis and Applications. Uploaded in accordance with the publisher's self-archiving policies.


  • quantum operations
  • von Neumann entropy
  • Yuan Li

    Paul Busch (Host)

    1 Sep 201231 Aug 2013

    Activity: Hosting a visitorAcademic


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