We review the continuous monitoring of a qubit through its spontaneous emission, at an introductory level. Contemporary experiments have been able to collect the fluorescence of an artificial atom in a cavity and transmission line, and then make measurements of that emission to obtain diffusive quantum trajectories in the qubit's state. We give a straightforward theoretical overview of such scenarios, using a framework based on Kraus operators derived from a Bayesian update concept; we apply this flexible framework across common types of measurements including photodetection, homodyne, and heterodyne monitoring and illustrate its equivalence to the stochastic master equation formalism throughout. Special emphasis is given to homodyne (phase-sensitive) monitoring of fluorescence. The examples we develop are used to illustrate basic methods in quantum trajectories, but also to introduce some more advanced topics of contemporary interest, including the arrow of time in quantum measurement, and trajectories following optimal measurement records derived from a variational principle. The derivations we perform lead directly from the development of a simple model to an understanding of recent experimental results.

中文翻译：

---

测量荧光以跟踪量子发射器的状态：理论综述

我们在介绍性层面回顾了通过自发发射对量子比特的连续监测。当代实验已经能够在腔体和传输线中收集人造原子的荧光，然后测量该发射以获得量子位状态下的扩散量子轨迹。我们使用基于从贝叶斯更新概念派生的克劳斯算子的框架，对此类场景进行了直接的理论概述；我们将这种灵活的框架应用于常见类型的测量，包括光电检测、零差和外差监测，并在整个过程中说明其与随机主方程形式主义的等效性。特别强调零差（相位敏感）荧光监测。我们开发的示例用于说明量子轨迹的基本方法，但也介绍了一些当代感兴趣的更高级的主题，包括量子测量中的时间箭头，以及遵循从变分原理导出的最佳测量记录的轨迹。我们执行的推导直接从简单模型的开发到对最近实验结果的理解。