Inferring an optimal Fisher measure

TL;DR

This paper introduces a method to infer the optimal Fisher information measure compatible with prior information using the virial theorem, avoiding explicit solutions of Schrödinger's equation, and providing analytic solutions for minimal FIM.

Contribution

It presents a novel approach to determine the optimal Fisher information measure directly from prior constraints without solving Schrödinger's equation explicitly.

Findings

Analytic solutions for the minimal Fisher information measure.

A new method linking the virial theorem to Fisher information.

Efficient inference of FIM based on prior information constraints.

Abstract

It is well known that a suggestive relation exists that links Schr\"odinger's equation (SE) to the information-optimizing principle based on Fisher's information measure (FIM). We explore here an approach that will allow one to infer the optimal FIM compatible with a given amount of prior information without explicitly solving first the associated SE. This technique is based on the virial theorem and it provides analytic solutions for the physically relevant FIM, that which is minimal subject to the constraints posed by the prior information.