SUFFICIENCY IN QUANTUM STATISTICAL INFERENCE: A SURVEY WITH EXAMPLES-Reference-Cited by-同舟云学术

SUFFICIENCY IN QUANTUM STATISTICAL INFERENCE: A SURVEY WITH EXAMPLES

Published:2006-09 Issue:03 Volume:09 Page:331-351
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

JENČOVÁ ANNA¹,PETZ DÉNES²

Affiliation:

1. Mathematical Institute, Slovak Academy of Sciences, Stefanikova 49, Bratislava, Slovakia

2. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, P. O. Box 127, H-1364 Budapest, Hungary

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

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

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219025706002408

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