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Journal | Journal of mathematical analysis and applications |
---|---|

Date | E-pub ahead of print - 15 Jun 2013 |

Date | Published (current) - 1 Dec 2013 |

Issue number | 1 |

Volume | 408 |

Number of pages | 10 |

Pages (from-to) | 384-393 |

Early online date | 15/06/13 |

Original language | English |

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*.

© 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

## Yuan Li

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