Statistical Theory of Quantum Controlled Dynamics

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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.