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We derive the form of the quantum filter equation describing the continuous observation of the phase of a quantum system in an arm of an interferometer via non-demolition measurements when the statistics of an input field used for the indirect measurement are in a general coherent state. Both quadrature homodyne detection and photon-counting dection schemes are covered, and we solve the linearized filter for a specific application.
We propose and experimentally demonstrate non-destructive and noiseless removal (filtering) of vacuum states from an arbitrary set of coherent states of continuous variable systems. Errors i.e. vacuum states in the quantum information are diagnosed t
We report a theoretical and experimental study on the role of indistinguishability in the estimation of an interferometric phase. In particular, we show that the quantum Fisher information, which limits the maximum precision achievable in the paramet
We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum estimation algor
In this paper, we investigate the problem of estimating the phase of a coherent state in the presence of unavoidable noisy quantum states. These unwarranted quantum states are represented by outlier quantum states in this study. We first present a st
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