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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*.
|Number of pages||10|
|Journal||Journal of mathematical analysis and applications|
|Early online date||15 Jun 2013|
|Publication status||Published - 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
- 1 Academic
Paul Busch (Host)1 Sep 2012 → 31 Aug 2013
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