A Mixed-Entropic Uncertainty Relation

TL;DR

This paper introduces a new uncertainty relation combining Shannon and Fisher information measures, offering advantages such as no need for Fourier transforms and increased sensitivity in position-momentum analysis.

Contribution

It proposes a mixed-entropic uncertainty relation that enhances traditional formulations by integrating Shannon and Fisher measures without Fourier transforms.

Findings

Provides a more sensitive uncertainty relation

Eliminates the need for Fourier transformation

Highlights advantages of combined Shannon and Fisher measures

Abstract

We highlight the advantages of using simultaneously the Shannon and Fisher information measures in providing a useful form of the uncertainty relation for the position-momentum case. It does not require any Fourier transformation. The sensitivity is also noteworthy.