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The purpose of this paper is to provide a concise review of the theory of unsharp measurements and its utility for high-fidelity state monitoring of a dynamic quantum system. Unsharp measurements are a special set of generalised measurements that have a weaker influence on the state of a system than projective measurements. We review a method for the estimation and control of a dynamic two-level system via unsharp measurements and show that finite estimation fidelity is obtained even in the presence of external noise.
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