Comment on "Noise and Disturbance in Quantum Measurements: An Information-Theoretic Approach"

TL;DR

This paper critiques a previous work on quantum measurement error and disturbance, clarifying the authors' misrepresentations and emphasizing the importance of error-disturbance relations for both state-dependent and state-independent measures.

Contribution

It corrects mischaracterizations of operational measures and clarifies the roles of error-disturbance relations in quantum measurements.

Findings

Clarifies the operational significance of error and disturbance measures.

Highlights the importance of error-disturbance relations for different measure types.

Points out inconsistencies in the previous work's claims.

Abstract

In this comment on the work of F. Buscemi, M.J.W. Hall, M. Ozawa and M.M. Wilde [PRL 112, 050401, 2014, arXiv:1310.6603], we point out a misrepresentation of measures of error and disturbance introduced in our recent work [PRL 111, 160405, 2013, arXiv:1306.1565] as being "purely formal, with no operational counterparts". We also exhibit an tension in the authors' message, in that their main result is an error-disturbance relation for state-independent measures, but its importance is declared to be limited to discrete variables. In contrast, we point out the separate roles played by such relations for either state-dependent or state-independent measures of error and disturbance.