Differential geometric aspects of parametric estimation theory for states on finite-dimensional C-algebras

A geometrical formulation of estimation theory for finite-dimensional \(C^{\star}\)-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer-Rao and Helstrom bounds for parametric statistical...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2020-11
Main Authors: Ciaglia, Florio M, Jost, Jürgen, Lorenz Schwachhöfer
Format: Article
Language:English
Subjects:
Differential geometry
Parameter estimation
Statistical models
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A geometrical formulation of estimation theory for finite-dimensional \(C^{\star}\)-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer-Rao and Helstrom bounds for parametric statistical models with discrete and finite outcome spaces is presented.
ISSN:2331-8422
DOI:10.48550/arxiv.2010.14394