Role of flow of information in the speedup of quantum evolution

The quantum evolution can be accelerated in non-Markovian environment. Previous results showed that the formation of 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 qubit driven by a classical field and coupled to a photonic crystal waveguide in the presence of a mirror. The perfect mirror can force part of the emitted light to return back to the qubit, and thus induce non-Markovian dynamics. Within the considered model, we show how the evolution speed is influenced by the memory time and the classical driving strength. In particular, we find that the formation of 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 to other non-Markovian environments.