### Abstract

Convexity properties of entropy-like functionals on states of a finite dimensional algebra are discussed. The treatment covers both the quantum mechanical and the classical cases. The purpose is to generalize Lieb's convexity theorem and the monotonicity of the relative entropy using the Jensen inequality of operator convex functions. From the quasi-entropies defined here the quantum version of Rényi's α- entropies can be deduced.

Original language | English |
---|---|

Pages (from-to) | 57-65 |

Number of pages | 9 |

Journal | Reports on Mathematical Physics |

Volume | 23 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1986 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics

### Cite this

**Quasi-entropies for finite quantum systems.** / Petz, D.

Research output: Contribution to journal › Article

*Reports on Mathematical Physics*, vol. 23, no. 1, pp. 57-65. https://doi.org/10.1016/0034-4877(86)90067-4

}

TY - JOUR

T1 - Quasi-entropies for finite quantum systems

AU - Petz, D.

PY - 1986

Y1 - 1986

N2 - Convexity properties of entropy-like functionals on states of a finite dimensional algebra are discussed. The treatment covers both the quantum mechanical and the classical cases. The purpose is to generalize Lieb's convexity theorem and the monotonicity of the relative entropy using the Jensen inequality of operator convex functions. From the quasi-entropies defined here the quantum version of Rényi's α- entropies can be deduced.

AB - Convexity properties of entropy-like functionals on states of a finite dimensional algebra are discussed. The treatment covers both the quantum mechanical and the classical cases. The purpose is to generalize Lieb's convexity theorem and the monotonicity of the relative entropy using the Jensen inequality of operator convex functions. From the quasi-entropies defined here the quantum version of Rényi's α- entropies can be deduced.

UR - http://www.scopus.com/inward/record.url?scp=0002988067&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002988067&partnerID=8YFLogxK

U2 - 10.1016/0034-4877(86)90067-4

DO - 10.1016/0034-4877(86)90067-4

M3 - Article

VL - 23

SP - 57

EP - 65

JO - Reports on Mathematical Physics

JF - Reports on Mathematical Physics

SN - 0034-4877

IS - 1

ER -