Quantum stochastic phase estimation has many applications in the precise measurement of various physical parameters. Similar to the estimation of a constant phase, there is a standard quantum limit for stochastic phase estimation, which can be obtained with the Mach–Zehnder interferometer and coherent input state. Recently, it has been shown that the stochastic standard quantum limit can be surpassed with nonclassical resources such as squeezed light. However, practical methods to achieve quantum enhancement in the stochastic phase estimation remain largely unexplored. Here we propose a method utilizing the SU(1,1) interferometer and coherent input states to estimate a stochastic optical phase. As an example, we investigate the Ornstein–Uhlenback stochastic phase. We analyze the performance of this method for three key estimation problems: prediction, tracking, and smoothing. The results show significant reduction of the mean square error compared with the Mach–Zehnder interferometer under the same photon number flux inside the interferometers. In particular, we show that the method with the SU(1,1) interferometer can achieve fundamental quantum scaling, achieve stochastic Heisenberg scaling, and surpass the precision of the canonical measurement.

中文翻译：

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使用 SU(1,1) 干涉仪进行量子增强随机相位估计

量子随机相位估计在各种物理参数的精确测量中有许多应用。与恒定相位的估计类似，随机相位估计也有一个标准的量子极限，可以通过 Mach-Zehnder 干涉仪和相干输入态获得。最近，研究表明，非经典资源（例如压缩光）可以超越随机标准量子极限。然而，在随机相位估计中实现量子增强的实用方法在很大程度上仍未得到探索。在这里，我们提出了一种利用 SU(1,1) 干涉仪和相干输入状态来估计随机光学相位的方法。例如，我们研究 Ornstein-Uhlenback 随机阶段。我们分析了该方法在三个关键估计问题上的性能：预测、跟踪和平滑。结果表明，在干涉仪内部相同的光子数通量下，与马赫-曾德干涉仪相比，均方误差显着降低。特别是，我们表明使用 SU(1,1) 干涉仪的方法可以实现基本量子标度，实现随机海森堡标度，并超过规范测量的精度。