We explore the general characteristics of a matter-wave Sagnac interferometer in a two-parameter estimation scheme. We find that the measurement precisions of both parameters cannot reach the Heisenberg limit (HL) simultaneously when the input state is maximally entangled. Only one of the parameters’ uncertainties can approach the HL while the other is scaled by the standard quantum limit. We provide the conditions with which the measurement precision of the specific parameter can reach the HL. We also discuss and figure out the concrete expressions of the constraint conditions for saturating the quantum Cramér–Rao bound. To satisfy these constraint conditions, the evolution time has to be a series of discrete values. Additionally, we calculate the variances of the parameters through some examples under these constraint conditions. The results provided in our work show some intrinsic features of the matter-wave Sagnac interferometer for the two-parameter estimation, which can be...

中文翻译：

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物质波Sagnac干涉仪中的两参数估计

我们在两参数估计方案中探索了物质波Sagnac干涉仪的一般特性。我们发现，当输入状态被最大程度地纠缠时，两个参数的测量精度无法同时达到海森堡极限（HL）。参数中只有一个不确定性可以接近HL，而另一个则由标准量子极限缩放。我们提供了特定参数的测量精度可以达到HL的条件。我们还将讨论并找出使量子Cramér-Rao界饱和的约束条件的具体表达式。为了满足这些约束条件，演化时间必须是一系列离散值。此外，我们通过一些示例在这些约束条件下计算参数的方差。