### Abstract

The Bregman operator divergence is introduced for density matrices by differentiation of the matrix-valued function x & x log x. This quantity is compared with the relative operator entropy of Fujii and Kamei. It turns out that the trace is the usual Umegaki's relative entropy which is the only intersection of the classes of quasi-entropies and Bregman divergences.

Original language | English |
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Pages (from-to) | 127-131 |

Number of pages | 5 |

Journal | Acta Mathematica Hungarica |

Volume | 116 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Jul 1 2007 |

### Keywords

- Bregman divergence
- F-divergence
- Quantum relative entropy

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Petz, D. (2007). Bregman divergence as relative operator entropy.

*Acta Mathematica Hungarica*,*116*(1-2), 127-131. https://doi.org/10.1007/s10474-007-6014-9