On two properties of the Fisher information

TL;DR

This paper provides alternative proofs for key properties of Fisher information, showing they can be understood as quantum kinetic energies, which has implications for understanding information measures in large systems.

Contribution

It introduces new proofs for superadditivity and affinity of Fisher information, linking them to quantum kinetic energy interpretations.

Findings

Fisher information exhibits superadditivity and affinity in large systems.

These properties can be derived from quantum kinetic energy interpretations.

The proofs offer new insights into the structure of Fisher information.

Abstract

Alternative proofs for the superadditivity and the affinity (in the large system limit) of the usual and some fractional Fisher informations of a probability density of many variables are provided. They are consequences of the fact that such informations can be interpreted as quantum kinetic energies.