Comment on "Uncertainty Relations for Positive Operator Valued Measures"

TL;DR

This paper critiques and clarifies previous entropic uncertainty relations for POVMs, correcting errors and emphasizing prior results to improve understanding of noise in quantum measurements.

Contribution

It provides corrections to existing entropic uncertainty bounds for POVMs and clarifies previous ambiguities in the literature.

Findings

Corrects errors in prior entropic bounds for POVMs

Highlights that some bounds were previously published

Clarifies the interpretation of key equations in the literature

Abstract

The principal aim of this Comment is to correct those entropic uncertainty relations that are presented in a paper by Massar [arXiv:quant-ph/0703036v2 (current version)], concerning two approaches to a study of the noise produced by POVM's. It is next emphasized that the first of the entropic bounds for POVM obtained by the above author has been already presented in Ref. [8]. Some exposition obscurity with equation (14) of the commented paper is elucidated. Finally, some more specific remarks on the paper content are given.