Improvement of Speed Limits: Quantum Effect on the Speed in Open Quantum Systems

Abstract: In the context of quantum speed limits, it has been shown that the minimum time required to cause a desired state conversion via the open quantum dynamics can be estimated using the entropy production. However, the established entropy-based bounds tend to be loose, making it difficult to accurately estimate the minimum time for evolution. In this research, we have combined the knowledge of the entropy-based speed limits with that of the resource theory of asymmetry (RTA) and provided much stricter inequalities. Our results show that the limitation on the change rate of states and expectation values can be divided into two parts: quantum coherence for energy (i.e., asymmetry) contributed by the system and the heat bath and the classical entropy-increasing effect from the bath. As a result, our inequalities demonstrate that the difference in the speed of evolution between classical and quantum open systems, i.e., the quantum enhancement in speed, is determined by the quantum Fisher information, which measures quantum fluctuations of energy and serves as a standard resource measure in the resource theory of asymmetry. We further show that a similar relation holds for the rate of change of expectation values of physical quantities.