Abstract
This article investigates the effects of input noise on a magnetometer with quantum feedback. Previous research has shown that feedback makes the measurement robust to an unknown parameter, the number of atoms involved, with the assumption that the feedback is noise free. To evaluate the effects of the feedback noise, we extend the original model by an input noise term. We then analyze the steady state performance of the Kalman filter for both the closed-loop and open-loop cases and retrieve the second moment of the estimation error. The results are compared and criteria for evaluating the effects of input noise are obtained. Robust and optimal designs are also discussed. Computations and simulations show how quantitatively the input noise increases the estimation error and changes the region where the closed-loop case behaves better than the open-loop case.
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