Comment on "Connection between entanglement and the speed of quantum evolution"

TL;DR

This paper discusses the limitations of previous studies on the relationship between entanglement and quantum evolution speed, highlighting the need to explore cases not covered earlier.

Contribution

It provides a critical comment on prior work, emphasizing the importance of analyzing all possible quantum states to understand entanglement's role in evolution speed.

Findings

Previous studies did not cover all bipartite states

The relation varies for uncovered cases

Highlights need for comprehensive analysis

Abstract

Batle et al. [Phys. Rev. A {\bf 72}, 032337 (2005)] and Borr\'{a}s et al. [Phys. Rev. A {\bf 74}, 022326 (2006)] studied the connection between entanglement and speed of quantum evolution for certain low-dimensional bipartite quantum states. However, their studies did not cover all possible cases. And the relation between entanglement and the maximum possible quantum evolution speed for these uncovered cases can very different from the ones that they have studied.