Clarke Claudia L, Ford Ian J
Department of Physics and Astronomy and London Centre for Nanotechnology, University College London, Gower Street, London WC1E 6BT, UK.
Entropy (Basel). 2024 Nov 26;26(12):1024. doi: 10.3390/e26121024.
The reduced density matrix that characterises the state of an open quantum system is a projection from the full density matrix of the quantum system and its environment, and there are many full density matrices consistent with a given reduced version. Without a specification of relevant details of the environment, the time evolution of a reduced density matrix is therefore typically unpredictable, even if the dynamics of the full density matrix are deterministic. With this in mind, we investigate a two-level open quantum system using a framework of quantum state diffusion. We consider the pseudorandom evolution of its reduced density matrix when subjected to an environment-driven process that performs a continuous quantum measurement of a system observable, invoking dynamics that asymptotically send the system to one of the relevant eigenstates. The unpredictability is characterised by a stochastic entropy production, the average of which corresponds to an increase in the subjective uncertainty of the quantum state adopted by the system and environment, given the underspecified dynamics. This differs from a change in von Neumann entropy, and can continue indefinitely as the system is guided towards an eigenstate. As one would expect, the simultaneous measurement of two non-commuting observables within the same framework does not send the system to an eigenstate. Instead, the probability density function describing the reduced density matrix of the system becomes stationary over a continuum of pure states, a situation characterised by zero further stochastic entropy production. Transitions between such stationary states, brought about by changes in the relative strengths of the two measurement processes, give rise to finite positive mean stochastic entropy production. The framework investigated can offer useful perspectives on both the dynamics and irreversible thermodynamics of measurement in quantum systems.
表征开放量子系统状态的约化密度矩阵是从量子系统及其环境的全密度矩阵投影而来的，并且有许多全密度矩阵与给定的约化版本一致。因此，如果没有对环境的相关细节进行明确说明，即使全密度矩阵的动力学是确定性的，约化密度矩阵的时间演化通常也是不可预测的。考虑到这一点，我们使用量子态扩散框架来研究一个两能级开放量子系统。我们考虑其约化密度矩阵在受到环境驱动过程影响时的伪随机演化，该过程对系统可观测量进行连续量子测量，并调用渐近地将系统发送到相关本征态之一的动力学。这种不可预测性由随机熵产生来表征，其平均值对应于系统和环境所采用的量子态主观不确定性的增加，这是由于动力学未充分指定所致。这与冯·诺依曼熵的变化不同，并且随着系统被引导至本征态，这种情况可以无限期持续。正如人们所预期的那样，在同一框架内对两个不对易可观测量的同时测量不会将系统发送到本征态。相反，描述系统约化密度矩阵的概率密度函数在一系列纯态上变得平稳，这种情况的特征是进一步的随机熵产生为零。由两个测量过程相对强度的变化引起的这种平稳态之间的跃迁会产生有限的正平均随机熵产生。所研究的框架可以为量子系统中测量的动力学和不可逆热力学提供有用的视角。
