Role of flow of information in the speedup of quantum evolution

Quantum evolution can be accelerated in a non-Markovian environment. Previous results show that the formation of a system-environment bound state governs the quantum speedup. Although a stronger bound state in the system-environment spectrum may seem like it should cause greater speed of evolution, this seemingly intuitive thinking may not always be correct. We illustrate this by investigating a classical-driven qubit interacting with a photonic crystal waveguide in the presence of a mirror, resulting in non-Markovian dynamics for the system. Within the considered model, we show the influence of the mirror and the classical field on the evolution speed of the system. In particular, we find that the formation of a bound state is not the essential reason for the acceleration of evolution. The quantum speedup is attributed to the flow of information, regardless of the direction in which the information flows. Our conclusion can also be used in other non-Markovian environments.