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In this paper, we investigate the problem of estimating the phase of acoherent state in the presence of unavoidable noisy quantum states. Theseunwarranted quantum states are represented by outlier quantum states in thisstudy. We first present a statistical framework of robust statistics in aquantum system to handle outlier quantum states. We then apply the method ofM-estimators to suppress untrusted measurement outcomes due to outlier quantumstates. Our proposal has the advantage over the classical methods in beingsystematic, easy to implement, and robust against occurrence of noisy states.

Robust phase estimation of Gaussian states in the presence of outlier quantum states