Von Neumann entropy and majorization
نویسنده
چکیده
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) = V ρV ∗.
منابع مشابه
Preprint Series 2012 / 2013 No : 11 Title : ‘ Von Neumann Entropy and Majorization ’ Author ( S )
In this paper, we firstly consider the properties of the Shannon entropy for two probability distributions which stand in the relationship of majorization. Then we give a generalized Uhlmann theorem in an infinite dimension Hilbert space. Also, we show that S(Φ(ρ)) = S(ρ) for all quantum states ρ if and only if there exists an isometry operator V such that Φ(ρ) = V ρV , where Φ is a quantum cha...
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