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.

中文翻译：

---

存在异常量子态时高斯态的稳健相位估计

在本文中，我们研究了在存在不可避免的噪声量子态的情况下估计相干态相位的问题。这些无根据的量子态在本研究中由离群量子态表示。我们首先在量子系统中提出了一个稳健统计的统计框架来处理异常量子态。然后，我们应用 M 估计器的方法来抑制由于异常量子态引起的不可信测量结果。我们的提议比经典方法具有系统性、易于实现和对噪声状态的发生具有鲁棒性的优势。