We predict that the phase-dependent error distribution of locally unentangled quantum states directly affects quantum parameter estimation accuracy. Therefore, we employ the displaced squeezed vacuum (DSV) state as a probe state and investigate an interesting question of the phase-sensitive nonclassical properties in the DSV’s metrology. We found that the accuracy limit of parameter estimation is a function of the phase-sensitive parameter $\phi - \theta /2$ with a period $\pi$. We show that when $\phi -\theta /2\ \in [ k\pi /2,3k\pi /4 )( k\in \mathbb{Z} )$, we can obtain the accuracy of parameter estimation approaching the ultimate quantum limit through the use of the DSV state with the larger displacement and squeezing strength, whereas when $\phi -\theta /2\ \in ( 3k\pi /4,k\pi ]( k\in \mathbb{Z} )$, the optimal estimation accuracy can be acquired only when the DSV state degenerates to a squeezed vacuum state.

中文翻译：

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压缩真空状态下量子计量学中的相敏非经典性质

我们预测局部非纠缠量子态的相位相关误差分布将直接影响量子参数估计的准确性。因此，我们采用位移压缩真空（DSV）状态作为探针状态，并研究了DSV计量学中有关相敏非经典特性的一个有趣问题。我们发现参数估计的精度极限是相位敏感参数$ \ phi-\ theta / 2 $的函数，周期为$ \ pi $。我们证明当$ \ phi-\ theta / 2 \ \ in [k \ pi / 2,3k \ pi / 4）（k \ in \ mathbb {Z}）$时，我们可以获得接近于通过使用具有较大位移和压缩强度的DSV态来获得最终的量子极限，而当$ \ phi-\ theta / 2 \ \ in（3k \ pi / 4，k \ pi]（k \ in \ mathbb {Z}）$，仅当DSV状态退化为压缩状态时，才能获得最佳估计精度真空状态。