Physical implications of Fisher-information's scaling symmetry

We study the scaling properties of Fisher's information measure (FIM) and show that from these one can straightforwardly deduce significant quantum-mechanical results. Specifically, we investigate the scaling properties of Fisher's measure I and encounter that, from the concomitant operati...

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Bibliographic Details
Authors: Flego, Silvana, Plastino, Ángel Luis, Plastino, Ángel Ricardo
Format: article
Status:Published version
Publication Date:2012
Country:Argentina
Institution:Universidad Nacional de La Plata
Repository:SEDICI (UNLP)
Language:English
OAI Identifier:oai:sedici.unlp.edu.ar:10915/84298
Online Access:http://sedici.unlp.edu.ar/handle/10915/84298
Access Level:Open access
Keyword:Física
Fisher Information
Legendre structure
reciprocity relations
scaling transform
Description
Summary:We study the scaling properties of Fisher's information measure (FIM) and show that from these one can straightforwardly deduce significant quantum-mechanical results. Specifically, we investigate the scaling properties of Fisher's measure I and encounter that, from the concomitant operating rules, several interesting, albeit known, results can be derived. This entails that such results can be regarded as pre-configured by the conjunction of scaling and information theory. The central notion to be arrived at is that scaling entails that I must obey a certain partial differential equation (PDE). These PDE-solutions have properties that enable the application of a Legendre-transform (LT). The conjunction PDE+LT leads one to obtain several quantum results without recourse to the Schrödinger's equation.