Phase estimation plays a central role in communications, sensing, and information processing. Quantum correlated states, such as squeezed states, enable phase estimation beyond the shot-noise limit, and in principle approach the ultimate quantum limit in precision, when paired with optimal quantum measurements. However, physical realizations of optimal quantum measurements for optical phase estimation with quantum-correlated states are still unknown. Here we address this problem by introducing an adaptive Gaussian measurement strategy for optical phase estimation with squeezed vacuum states that, by construction, approaches the quantum limit in precision. This strategy builds from a comprehensive set of locally optimal POVMs through rotations and homodyne measurements and uses the Adaptive Quantum State Estimation framework for optimizing the adaptive measurement process, which, under certain regularity conditions, guarantees asymptotic optimality for this quantum parameter estimation problem. As a result, the adaptive phase estimation strategy based on locally-optimal homodyne measurements achieves the quantum limit within the phase interval of $[0, \pi/2)$. Furthermore, we generalize this strategy by including heterodyne measurements, enabling phase estimation across the full range of phases from $[0, \pi)$, where squeezed vacuum allows for unambiguous phase encoding. Remarkably, for this phase interval, which is the maximum range of phases that can be encoded in squeezed vacuum, this estimation strategy maintains an asymptotic quantum-optimal performance, representing a significant advancement in quantum metrology.

中文翻译：

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接近量子极限的压缩真空的自适应相位估计


相位估计在通信、传感和信息处理中发挥着核心作用。量子相关态（例如压缩态）可以使相位估计超出散粒噪声极限，并且在与最佳量子测量相结合时，原则上精度接近最终量子极限。然而，利用量子相关态进行光学相位估计的最佳量子测量的物理实现仍然未知。在这里，我们通过引入一种自适应高斯测量策略来解决这个问题，该策略用于具有压缩真空态的光学相位估计，通过构造，精度接近量子极限。该策略通过旋转和零差测量从一组全面的局部最优 POVM 构建，并使用自适应量子状态估计框架来优化自适应测量过程，在某些规律性条件下，保证了该量子参数估计问题的渐近最优性。因此，基于局部最优零差测量的自适应相位估计策略在$[0,\pi/2)$相位区间内达到了量子极限。此外，我们通过包括外差测量来推广该策略，从而能够在从 $[0, \pi)$ 的整个相位范围内进行相位估计，其中压缩真空允许明确的相位编码。值得注意的是，对于这个相位间隔（可以在压缩真空中编码的最大相位范围），这种估计策略保持了渐近量子最优性能，代表了量子计量学的重大进步。