Reply to "Comment on 'Modified quantum-speed-limit bounds for open quantum dynamics in quantum channels'"

TL;DR

This paper defends the validity of certain quantum-speed-limit bounds against a comment claiming inconsistencies, demonstrating that the criticisms are unfounded and that the bounds remain reliable for numerical use.

Contribution

The authors clarify misconceptions about quantum-speed-limit bounds and show that the criticized inconsistencies are either similar or unavoidable, reaffirming the bounds' validity.

Findings

All QSL bounds in question are essentially similar.

The alleged inconsistency in the comment's original paper is invalid.

An unavoidable inconsistency exists in the comment's example.

Abstract

The authors of the comment[Phys. Rev. A 97, 046101 (2018)] raise that the inconsistency in calculating some common quantum-speed-limit (QSL) bounds, which is presented in our paper [Phys. Rev. A 95, 052118 (2017)], does not exist in their paper [Phys. Rev. A 94, 052125 (2016)]. Therefore they insist that their criticism to some QSL bounds is still valid. We demonstrate all the QSL bounds mentioned in the comment are similar in essence. We also show the inconsistency which is presented in their original paper can not be used to support their criticism. Furthermore, we exhibit although the inconsistency presented in our paper is not a same one to which is presented by the authors of the comment, it exists and be unavoidable in their example. Accordingly, we believe the result in our paper is usable in numerical calculations.