The identification of time-varying parameters (e.g., directly inaccessible in situ signals in vacuum and low-temperature environments) is prevalent for characterizing the dynamics of quantum processes. Under certain circumstances, they can be identified from time-resolved measurements via Ramsey interferometry experiments, but only with specially designed probe systems can the parameters be explicitly read out, and a rigorous identifiability analysis is lacking, i.e., whether the measurement data are sufficient for unambiguous identification. In this paper we formulate this problem as the invertibility of the input-output mapping associated with the quantum system for which an algebraic identifiability criterion is derived based on the system's relative degree. The invertibility analysis also leads to an inversion-based algorithm for numerically identifying the parameters, which is computationally much more efficient than nonlinear regression methods. The effectiveness of the criterion are demonstrated by numerical examples.

中文翻译：

---

量子系统中时变信号的识别

时变参数的识别（例如，原位直接无法访问）真空和低温环境中的信号）是表征量子过程动力学的普遍方法。在某些情况下，可以通过Ramsey干涉仪实验从时间分辨的测量中识别出它们，但是只有使用专门设计的探针系统才能明确读出参数，并且缺乏严格的可识别性分析，即，测量数据是否足够用于明确的识别。在本文中，我们将此问题表示为与量子系统相关的输入-输出映射的可逆性，基于该系统的相对程度，导出了一个代数可识别性准则。可逆性分析还得出了一种基于反演的算法，用于对参数进行数字识别，在计算上比非线性回归方法有效得多。数值实例证明了该准则的有效性。