The identification of mean quantum potential with Fisher information leads to a strong uncertainty relation

TL;DR

This paper demonstrates that equating the mean quantum potential with Fisher information yields a stronger uncertainty relation than traditional quantum bounds, offering a new perspective on quantum mechanics and potential experimental tests.

Contribution

It introduces a novel link between the mean quantum potential and Fisher information, resulting in a stronger uncertainty principle than existing formulations.

Findings

Derives a new uncertainty relation from Fisher information and quantum potential

Shows the relation can be experimentally tested

Provides a theoretical basis for a stronger quantum uncertainty bound

Abstract

The Cramer-Rao bound, satisfied by classical Fisher information, a key quantity in information theory, has been shown in different contexts to give rise to the Heisenberg uncertainty principle of quantum mechanics. In this paper, we show that the identification of the mean quantum potential, an important notion in Bohmian mechanics, with the Fisher information, leads, through the Cramer-Rao bound, to an uncertainty principle which is stronger, in general, than both Heisenberg and Robertson-Schrodinger uncertainty relations, allowing to experimentally test the validity of such an identification.