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量子速率极限给出了量子系统演化的最大速率，表征了量子系统从初态到末态动力学演化的时间下界。量子速率极限在量子光学、量子信息、量子计算、量子测量、量子计量学和纳米尺度热力学等前沿物理研究领域中具有重要作用。在本篇综述中，我们对量子速率极限的建立和发展历程进行回顾，总结该领域的一些重要研究成果，阐述其在一些前沿研究领域中的重要应用。首先，我们分别对封闭量子系统和开放量子系统，总结近年来发展的各类量子速率极限时间界，并介绍以此为基础的量子速率极限时间统一界。随后，我们介绍基于微分几何方法建立的量子速率极限，并介绍一类用几何相位变化率构造的量子速率极限界——平行传输速率极限界，以及在相位框架下的量子速率极限统一界。然后，我们介绍量子相空间中的动力学演化速率极限，以及应用轨线方法揭示量子速率极限的统计性质。最后，我们阐述了量子速率极限在一些前沿研究领域，如量子计算、量子控制、量子热力学等中的重要应用。
Abstract：The quantum speed limit(QSL) defines the maximum speed of the evolution for a quantum system, and it establishes the minimum time required for dynamical evolution of a quantum system from an initial state to a final state. It holds significant theoretical and practical importance in various advanced fields of physics, including quantum optics, quantum information, quantum computing, quantum measurement, quantum metrology, and nanoscale thermodynamics. This review offers a systematic overview of the formulations and development of QSL bounds recently, summarizes key research findings in this domain, and discusses its critical applications in cutting-edge research areas. First, we outline various QSL bounds proposed for both closed and open quantum systems in recent years and present a unified bound derived from these formulations. Subsequently, we discuss the QSL bounds established through differential geometry, a class of bounds constructed based on the rate of change of geometric phases, and the speed limit bound defined within the phase framework. Furthermore, we explore the QSL for dynamical evolution in quantum phase space and analyze its statistical behavior using trajectory-based methods. Finally, we discuss its essential applications in prominent research fields such as quantum computing, quantum control, and quantum thermodynamics.
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基本信息:
DOI：
中图分类号:O413
引用信息:
[1]杨道霖,蔡祥吉,彭勇刚,等.量子系统动力学演化速率极限[J].山东师范大学学报(自然科学版),2025,40(04):289-324.
基金信息:
国家自然科学基金资助项目(12234013,12174221)