### Abstract

This paper attempts to give an overview about sufficiency in the setting of quantum statistics. The basic concepts are treated in parallel to the measure theoretic case. It turns out that several classical examples and results have a noncommutative analogue. Some of the results are presented without proof (but with exact references) and the presentation is intended to be self-contained. The main examples discussed in the paper are related to the Weyl algebra and to the exponential family of states. The characterization of sufficiency in terms of quantum Fisher information is a new result.

Original language | English |
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Pages (from-to) | 331-351 |

Number of pages | 21 |

Journal | Infinite Dimensional Analysis, Quantum Probability and Related Topics |

Volume | 9 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 1 2006 |

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### Keywords

- Coarse-graining
- Exponential family
- Factorization theorem
- Perturbation of states
- Quantum Fisher information
- Quantum statistics
- Sufficient subalgebra

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Mathematical Physics
- Applied Mathematics