Comment on "Uncertainty relations in terms of the Tsallis entropy

TL;DR

This paper critically examines a recent claim about uncertainty relations involving Tsallis entropy, demonstrating that the proposed inequality is invalid and highlighting that the problem of improving bounds remains unresolved.

Contribution

It provides a rigorous proof that a recent inequality used in uncertainty relations with Tsallis entropy is invalid, emphasizing the need for further research.

Findings

The inequality used by Wilk and W{}ordarczyk is invalid.

The problem of improving bounds in uncertainty relations remains unsolved.

The original bounds in the 2006 paper still stand as the best known.

Abstract

We prove that the inequality used recently by Wilk and W{\l}odarczyk [Phys. Rev. A {\bf 79}, 062108 (2009)] to find a better lower bound in the uncertainty relations for the R\'enyi entropies is invalid. Thus, the problem of improving the bound given in our paper [Phys. Rev. A {\bf 74}, 052101 (2006)] remains unsolved.