Statistical Theory of Quantum Controlled Dynamics

量子开放系统的建模、估计和识别是一系列量子工程任务的关键使能工具，例如状态准备和层析、量子反馈控制、误差校正和高精度计量。随着量子设备和测量技术变得越来越复杂，实验人员必须解释越来越复杂的测量数据集，以获得有关系统状态和动力学的准确信息。因此，有必要将量子统计的数学基础扩展到传统的I.I.D.之外。状态估计框架，以解决涉及相互作用系统的相关状态的新推理问题，具有真实的噪声建模和最优实验设计。这个博士项目的目标是在量子投入产出(I-O)动力学的框架下建立量子随机过程的统计理论。I-O形式主义将感兴趣的系统(例如量子设备或传感器)描述为通过输入和输出通道与外部世界交互的黑匣子。中心前提是关于动力学的信息被连续编码到输出状态，并且可以利用这些资源来执行诸如系统识别、估计和量子增强计量等任务。

The modelling, estimation and identification of quantum open systems are key enabling tools for a broad array of quantum engineering tasks such as state preparation and tomography, quantum feedback control, error correction, and high precision metrology. As quantum devices and measurement techniques become more sophisticated, experimenters have to interpret increasingly complex measurement datasets to obtain accurate information about the system's state and dynamics. Therefore, there is a need for expanding the mathematical foundations of quantum statistics beyond the traditional i.i.d. framework of state estimation, in order to tackle new inference problems involving correlated states of interacting systems, with realistic modelling of noise, and optimal experimental design. The goal of this PhD project is to build a statistical theory of quantum stochastic processes in the framework of quantum input-output (I-O) dynamics. The I-O formalism describes the system of interest (e.g. quantum device, or sensor) as a black-box interacting with the outside world via input and output channels. The central premise is that information about the dynamics is continuously encoded into the output state, and this resource can be exploited to perform tasks such as system identification, estimation and quantum enhanced metrology.