A non-Markovianity measure based on quantum speed limit

Abstract

The quantum speed limit sets a fundamental bound on the speed at which quantum states can evolve and is commonly regarded as a manifestation of the time-energy uncertainty relation. In contrast, non-Markovian dynamics arise in open quantum systems when past interactions with the environment influence the system’s evolution. Establishing connections between these two concepts is a key challenge in quantum information science. By leveraging the relationship between non-Markovianity and Bures distance metrics, we propose a novel approach to quantify non-Markovianity through quantum speed limit. This method incorporates the impact of the quantum speed limit time on non-Markovian dynamics. As applications, we analyze the Jaynes–Cummings and damped Jaynes–Cummings models, demonstrating how system-environment interactions shape non-Markovian behavior. Our results reveal that the non-Markovian character of these processes is strongly correlated with a reduction in the quantum speed limit time, signifying a speedup in quantum evolution.