On hybrid quantum filtering and capability of quantum sensors

This dissertation focuses on quantum filtering and quantum sensing. To exploit or manipulate a quantum system, it is nontrivial to thoroughly investigate the information carried by limited observations. In particular, our research spans two problems: quantum hybrid filtering for systems subject to classical disturbances; the determination of the capability of a class of quantum sensors, guided by the research goal of laying a solid and comprehensive foundation in quantum engineering. The first topic is the hybrid filtering problem where the goal is to derive a filter for a class of quantum systems whose dynamics consist of both a quantum part and a classical part. Another topic is to analyse the information extraction capability of a specially designed qubit sensor over a spin-1/2 chain system. Part I of the dissertation studies a class of hybrid filtering problems where a quantum system is subject to a classical stochastic signal. The task is to obtain a filter which is able to estimate both the quantum system state and the classical signal simultaneously. One major challenge is to describe the dynamics of a quantum system and a classical signal within a uniform probability space. Our solution is to represent the classical disturbing signal by an analog cavity system. A composite quantum analog system is then employed to represent the hybrid quantum-classical model. The purpose is to make use of the quantum filtering theory to obtain an SME filter with necessary modifications. Given such a filter for the quantum analog system, estimates of the quantities in the initial hybrid system can be inferred. The idea is successfully demonstrated under two situations: the object quantum system is a qubit system; the object quantum system is a cavity system. Part II of the dissertation investigates the capability of a class of qubit sensors. We employ qubit detectors to extract information of a spin chain system with unknown structure parameters. The measurement data provided by qubit detectors is then processed to infer parameter information. The capability of a sensor is defined as the ability of estimating all the unknown parameters. Two analysis methods, including the similarity transformation approach and the Grobner basis method, are employed to evaluate the capability. We show that there is an improvement on the sensing capability by increasing the number of sensing qubits under several measurement schemes.