Sufficiency in quantum statistical inference. A survey with examples

Anna Jenčová, Dénes Petz

Research output: Contribution to journalArticle

17 Citations (Scopus)

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 languageEnglish
Pages (from-to)331-351
Number of pages21
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Volume9
Issue number3
DOIs
Publication statusPublished - 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

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