Comment on "Improved bounds on entropic uncertainty relations"

TL;DR

This paper analytically proves entropic uncertainty relations and corrects a mistake in a previous derivation, ensuring the constraints are properly considered for accurate results.

Contribution

It provides an analytical proof of existing entropic uncertainty relations and clarifies errors in prior work caused by improper constraint handling.

Findings

Confirmed the validity of the entropic uncertainty relations.

Identified and corrected a mistake in the previous derivation.

Ensured proper consideration of problem constraints in the proof.

Abstract

We provide an analytical proof of the entropic uncertainty relations presented by de Vicente and Sanchez-Ruiz in [Phys. Rev. A 77, 042110 (2008)] and also show that the replacement of Eq. (27) by Eq. (29) in that reference introduces solutions that do not take fully into account the contraints of the problem, which in turn leads to some mistakes in their treatment.