Quantum speed limit from a quantum-state-diffusion method

TL;DR

This paper introduces a new quantum speed limit bound for open systems based on a quantum-state-diffusion approach, revealing how environment interactions affect the system's maximum evolution speed and offering insights for quantum control.

Contribution

It proposes a novel QSL bound from the total system perspective, extending previous methods and highlighting the role of non-Markovian dynamics and bound states in quantum speed limits.

Findings

Infinite speedup capacity in noiseless case

Environment destroys speedup under Markovian approximation

Non-Markovian dynamics can recover speedup with bound states

Abstract

Characterizing the most efficient evolution, the quantum speed limit (QSL) plays a significant role in quantum technology. How to generalize the well-established QSL from closed systems to open systems has attracted much attention. In contrast to the previous schemes to derive the QSL from the reduced dynamics of open system, we propose a QSL bound from the point of view of the total system consisting of the open system and its environment using a quantum-state-diffusion method. The application of our scheme to a two-level system reveals that the system possesses an infinite speedup capacity in the noiseless case, which is destroyed by the environment under the Born-Markovian approximation. It is interesting to find that the capacity in the noiseless case is recovered in the non-Markovian dynamics as long as a bound state is formed in the energy spectrum of the total system. Enriching the characterization schemes of the QSL, our result provides an efficient way to control the QSL of open systems.