We propose an analogue of $\text{SU}(1,1)$ interferometry to measure rotation of a spin by using two-spin squeezed states. Attainability of the Heisenberg limit for the estimation of the rotation angle is demonstrated for maximal squeezing. For a specific direction and strength an advantage in sensitivity for $all$ equatorial rotation axes (and hence non-commuting rotations) over the classical bound is shown in terms of quadratic scaling of the single-parameter quantum Fisher information for the corresponding rotation angles. Our results provide a method for measuring magnetic fields in any direction in the $x$-$y$-plane with the same optimized initial state.

中文翻译：

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自旋非通勤旋转的最小噪声估计

我们提出了一种类似于 $\text{SU}(1,1)$ 干涉测量法，通过使用双自旋压缩态来测量自旋的旋转。对于最大挤压，证明了旋转角度估计的海森堡极限的可达性。对于特定方向和强度，$all$ 赤道旋转轴（以及因此非通勤旋转）相对于经典界限的灵敏度优势通过对应旋转角度的单参数量子费希尔信息的二次缩放来显示。我们的结果提供了一种在具有相同优化初始状态的情况下测量 $x$-$y$ 平面中任何方向的磁场的方法。