Quantum speed limit time for open quantum systems: different metrics perspective

In this paper, we investigate the quantum speed limit time for open quantum systems by exploiting a geometric approach which provided by the Bures distance and the sine distance as the distance measures between initial and final states of a quantum system. By comparing the obtained results with the results of previous work obtained by the Bures angle, we demonstrate that the Bures distance provides the sharpest quantum speed limit time bound in comparison to the sine distance and Bures angle. Therefore, it leads to the fastest quantum evolution when the reservoir enters to the non-Markovian region.