Abstract
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.
Highlights
One of the challenges in developing quantum information technologies is to suppress uncontrollable elements in both classical and quantum devices
We develop a statistical framework to handle certain types of state preparation and measurement (SPAM) errors by applying robust statistics [4,5,6,7,8]
We studied the problem of phase estimation for coherent states in the presence of unavoidable outlier quantum states
Summary
One of the challenges in developing quantum information technologies is to suppress uncontrollable elements in both classical and quantum devices. We demonstrate the usefulness and effectiveness of robust statistics in the quantum case To this end, we consider a specific problem—phase estimation of coherent states in the presence of outlier quantum states. The model studied in this paper is not described by a unital CP-TP map, but a mixture of different quantum gaussian states Another distinction is that we do not need to assume a specific form for outlier quantum states when applying our method to real data. The proposed method of M-estimators can be applied to the occurrence of unknown noisy quantum states This is one of the practical advantages of the theory of robust statistics.
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