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access icon openaccess Estimating Hamiltonian fluctuations from quantum time averages

This study presents a framework for the enhancement of parameter estimation issues by computing the time average of several quantum observables measured under the evolution of the Hamiltonian system. These time-cum-quantum averages are expressed as a quadratic function of the orthogonal projections on the eigen subspaces of the system. Estimation of the parameters is done using the approximate time-independent perturbation theory assuming the other parameters to be small with respect to one of the parameters that is normalised to unity in the presence of noise. The study also proves that the derived expression for the mean square parameter estimation error attains the quantum limit. When the measurement noise is classical and for general positive operator-valued measure successive time, the authors derive an expression for the quantum Cramèr–Rao lower bound.

http://iet.metastore.ingenta.com/content/journals/10.1049/iet-qtc.2020.0001
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