Comment on “Connection between entanglement and the speed of quantum evolution” and on “Entanglement and the lower bounds on the speed of quantum evolution”

Abstract

Batle et al. [Phys. Rev. A 72, 032337 (2005)] and Borr\'as et al. [Phys. Rev. A 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 be very different from the ones that they have studied.