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Parameter estimation and control in a QKD link

We describe a technique of parameter estimation and control in a phase-encoded quantum key distribution that uses continuous control of receiver-interferometer differential path length to maintain alignment with the transmitter. In this fiber-based system, a small number of training frames are sent over the quantum channel allowing the receiver to compensate for drift in the transmitter and receiver interferometers due to slow changes in temperature. The minimum mean-square error estimation method used to infer the state of the system incorporates the prior knowledge of the fiber dynamics recursively. The optimal linear-quadratic regulator feedback design is described and combined with the estimator to obtain the stochastic linear regulator of the path-length error.