We identify the large-$N$ scaling of the metrological quantum gain offered by over-squeezed spin states that are accessible by one-axis twisting, as a function of the preparation time. We further determine how the scaling is modified by relevant decoherence processes and predict a discontinuous change of the quantum gain at a critical preparation time that depends on the noise. Our analytical results provide recipes for optimal and feasible implementations of quantum enhancements with non-Gaussian spin states in existing experiments, well beyond the reach of spin squeezing.

中文翻译：

---

非高斯自旋态灵敏度增强的标度定律

我们确定了大$N$作为准备时间的函数，可通过单轴扭曲获得的过度压缩自旋态提供的计量量子增益的缩放。我们进一步确定相关退相干过程如何修改缩放，并预测在关键准备时间量子增益的不连续变化，这取决于噪声。我们的分析结果为现有实验中非高斯自旋态量子增强的最佳和可行实现提供了方法，远远超出了自旋压缩的范围。