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