We investigate the impact of dissipation, including energy relaxation and decoherence, on weak measurements. While weak measurements have been successful in signal amplification, dissipation can compromise their usefulness. More precisely, we show that in systems with a unique steady state, weak values always converge to an expectation value of the measured observable as dissipation time tends to infinity, in contrast to systems with multiple steady states, where the weak values can remain anomalous, i.e. outside the range of eigenvalues of the observable, even in the limit of an infinite dissipation time. In addition, we propose a method for extracting information about the dissipative dynamics of a system using weak values at short dissipation times. Specifically, we explore the amplification of the dissipation rate in a two-level system and the use of weak values to differentiate between Markovian and non-Markovian dissipative dynamics. We also find that weak measurements operating around a weak atom-cavity coupling can probe the atom dissipation through the weak value of non-Hermitian operators within the rotating-wave approximation of the weak interaction.

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关于耗散量子系统中弱测量的相关性

我们研究耗散（包括能量弛豫和退相干）对弱测量的影响。虽然弱测量在信号放大方面取得了成功，但耗散可能会影响其实用性。更准确地说，我们表明，在具有独特稳态的系统中，当耗散时间趋于无穷大时，弱值总是收敛到测量可观测值的期望值，与具有多个稳态的系统相反，其中弱值可以保持异常，即在可观察的特征值范围之外，即使在无限耗散时间的限制下。此外，我们提出了一种在短耗散时间内使用弱值提取有关系统耗散动力学信息的方法。具体来说，我们探索了两级系统中耗散率的放大以及使用弱值来区分马尔可夫和非马尔可夫耗散动力学。我们还发现，围绕弱原子腔耦合进行的弱测量可以通过弱相互作用的旋转波近似中非厄米算子的弱值来探测原子耗散。