Hasegawa Yoshihiko
Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.
Phys Rev Lett. 2021 Jan 8;126(1):010602. doi: 10.1103/PhysRevLett.126.010602.
We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the system-environment interaction, we bound the counting observables in the environment by the survival activity, which reduces to the dynamical activity in classical Markov processes. Remarkably, the relation derived herein holds for general open quantum systems with any counting observable and any initial state. Therefore, our relation is satisfied for classical Markov processes with arbitrary time-dependent transition rates and initial states. We apply our relation to continuous measurement and the quantum walk to find that the quantum nature of the system can enhance the precision. Moreover, we can make the lower bound arbitrarily small by employing appropriate continuous measurement.
我们推导了一般开放量子动力学的热力学不确定性关系，该动力学由一个包含系统和环境的复合系统上的联合幺正演化描述。通过在系统 - 环境相互作用后测量环境状态，我们用生存活性来限制环境中的计数可观测量，在经典马尔可夫过程中它简化为动力学活性。值得注意的是，本文推导的关系适用于具有任何计数可观测量和任何初始状态的一般开放量子系统。因此，对于具有任意时间依赖跃迁速率和初始状态的经典马尔可夫过程，我们的关系也成立。我们将我们的关系应用于连续测量和量子行走，发现系统的量子性质可以提高精度。此外，通过采用适当的连续测量，我们可以使下限任意小。
