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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*.
Original language | English |
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Pages (from-to) | 384-393 |
Number of pages | 10 |
Journal | Journal of mathematical analysis and applications |
Volume | 408 |
Issue number | 1 |
Early online date | 15 Jun 2013 |
DOIs | |
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.Keywords
- quantum operations
- von Neumann entropy
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