Van Vu Tan, Saito Keiji
Department of Physics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan.
Phys Rev Lett. 2022 Apr 8;128(14):140602. doi: 10.1103/PhysRevLett.128.140602.
The thermodynamic and kinetic uncertainty relations indicate trade-offs between the relative fluctuation of observables and thermodynamic quantities such as dissipation and dynamical activity. Although these relations have been well studied for classical systems, they remain largely unexplored in the quantum regime. In this Letter, we investigate such trade-off relations for Markovian open quantum systems whose underlying dynamics are quantum jumps, such as thermal processes and quantum measurement processes. Specifically, we derive finite-time lower bounds on the relative fluctuation of both dynamical observables and their first passage times for arbitrary initial states. The bounds imply that the precision of observables is constrained not only by thermodynamic quantities but also by quantum coherence. We find that the product of the relative fluctuation and entropy production or dynamical activity is enhanced by quantum coherence in a generic class of dissipative processes of systems with nondegenerate energy levels. Our findings provide insights into the survival of the classical uncertainty relations in quantum cases.
热力学和动力学不确定性关系表明，可观测量的相对涨落与诸如耗散和动力学活性等热力学量之间存在权衡。尽管这些关系在经典系统中已得到充分研究，但在量子领域仍 largely 未被探索。在本信函中，我们研究了底层动力学为量子跃迁的马尔可夫开放量子系统的这种权衡关系，例如热过程和量子测量过程。具体而言，我们针对任意初始态推导了动力学可观测量及其首次通过时间的相对涨落的有限时间下界。这些界意味着可观测量的精度不仅受到热力学量的约束，还受到量子相干性的约束。我们发现，在具有非简并能级的系统的一般耗散过程类别中，量子相干性增强了相对涨落与熵产生或动力学活性的乘积。我们的发现为经典不确定性关系在量子情形下的存续提供了见解。
