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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.
We propose a machine learning framework for parameter estimation of single mode Gaussian quantum states. Under a Bayesian framework, our approach estimates parameters of suitable prior distributions from measured data. For phase-space displacement an
We introduce a geometric quantification of quantum coherence in single-mode Gaussian states and we investigate the behavior of distance measures as functions of different physical parameters. In the case of squeezed thermal states, we observe that re
We calculate the quantum Cramer--Rao bound for the sensitivity with which one or several parameters, encoded in a general single-mode Gaussian state, can be estimated. This includes in particular the interesting case of mixed Gaussian states. We appl
We derive the form of the quantum filter equation describing the continuous observation of the phase of a quantum system in an arm of an interferometer via non-demolition measurements when the statistics of an input field used for the indirect measur
We address the estimation of the loss parameter of a bosonic channel probed by arbitrary signals. Unlike the optimal Gaussian probes, which can attain the ultimate bound on precision asymptotically either for very small or very large losses, we prove