Quantum speed limit of a noisy continuous-variable system

Setting the minimal-time bound for a quantum system to evolve between two distinguishable states, the quantum speed limit (QSL) characterizes the latent capability in speeding up of the system. It has found applications in determining the quantum superiority in many quantum technologies. However, previous results showed that such a speedup capability is generally destroyed by the environment induced decoherence in the Born-Markovian approximate dynamics. We here propose a scheme to recover the speedup capability in a dissipative continuous-variable system within the exact non-Markovian framework. It is found that the formation of a bound state in the energy spectrum of the total system consisting of the system and its environment can be used to restore the QSL to its noiseless performance. Giving an intrinsic mechanism in preserving the QSL, our scheme supplies a guideline to speed up certain quantum tasks in practical continuous-variable systems.