A characterization of extended monotone metrics
type: Item
instance of: scholarly article
title: A characterization of extended monotone metrics
zbMATH Open document ID: 1206.94016
author: Wataru Kumagai
published in: Linear Algebra and its Applications
publication date: 2010-12-01T00:00:00Z
review text: It is well-known that information geometry was initiated by S. Amari. In classical information geometry, the Fisher metric is characterized as Riemannian metric on the probability simplex. In quantum information geometry, D.Petz gave the monotone metric (quantum Fisher information) on quantum state space. In the present paper, the author gives the extension of Petz's result. That is, the characterization of the extended monotone metric on the set of all positive Hermitian matrices is given, as L. L. Campbell gave an extension of the characterization from probability simplex to positive cone in classical case.
reviewed by: Shigeru Furuichi
Mathematics Subject Classification ID: 94A17
zbMATH DE Number: 5821961
zbMATH Keywords: Fisher metric
zbMATH Keywords: monotone metric
zbMATH Keywords: quantum information geometry
zbMATH Keywords: operator monotone function
MaRDI profile type: Publication
full work available at URL: j.laa.2010.08.019
OpenAlex ID: W2087883876
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DOI: 10.1016/J.LAA.2010.08.019
description: scientific article; zbMATH DE number 5821961