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This dissertation explores the topics of parameter estimation and model reduction in the context of quantum filtering. Chapters 2 and 3 provide a review of classical and quantum probability theory, stochastic calculus and filtering. Chapter 4 studies the problem of quantum parameter estimation and introduces the quantum particle filter as a practical computational method for parameter estimation via continuous measurement. Chapter 5 applies these techniques in magnetometry and studies the estimators uncertainty scalings in a double-pass atomic magnetometer. Chapter 6 presents an efficient feedback controller for continuous-time quantum error correction. Chapter 7 presents an exact model of symmetric processes of collective qubit systems.
We investigate cryptographic quantum parameter estimation with a high-dimensional system that allows only Bob (Receiver) to access the result and achieve optimal parameter precision from Alice (Sender). Eavesdropper (Eve) only can disturb the paramet
We present a general framework for sensitivity optimization in quantum parameter estimation schemes based on continuous (indirect) observation of a dynamical system. As an illustrative example, we analyze the canonical scenario of monitoring the posi
We provide a general framework for handling the effects of a unitary disturbance on the estimation of the amplitude $lambda$ associated to a unitary dynamics. By computing an analytical and general expression for the quantum Fisher information, we pr
In this article we derive a measure of quantumness in quantum multi-parameter estimation problems. We can show that the ratio between the mean Uhlmann Curvature and the Fisher Information provides a figure of merit which estimates the amount of incom
Quantum metrology holds the promise of an early practical application of quantum technologies, in which measurements of physical quantities can be made with much greater precision than what is achievable with classical technologies. In this review, w