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**1 - 3**of**3**### Department of Mathematics PREPRINT SERIES 2012/2013 NO: 11 TITLE: ‘VON NEUMANN ENTROPY AND MAJORIZATION’

, 2012

"... Abstract: 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 ..."

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Abstract: 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) = VρV ∗ , where Φ is a quantum channel.