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Von Neumann entropy and majorization

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JournalJournal of mathematical analysis and applications
DateE-pub ahead of print - 15 Jun 2013
DatePublished (current) - 1 Dec 2013
Issue number1
Volume408
Number of pages10
Pages (from-to)384-393
Early online date15/06/13
Original languageEnglish

Abstract

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*.

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© 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.

    Research areas

  • quantum operations, von Neumann entropy

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  • Yuan Li

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