The weak value amplification technique has been proved useful for precision metrology in both theory and experiment. To explore the ultimate performance of weak value amplification for multi-parameter estimation, we investigate a general weak measurement formalism with assistance of high-order Hermite-Gaussian pointer and quantum Fisher information matrix. Theoretical analysis shows that the ultimate precision of our scheme is improved by a factor of square root of 2n+1, where n is the order of Hermite-Gaussian mode. Moreover, the parameters’ estimation precision can approach the precision limit with maximum likelihood estimation method and homodyne method. We have also given a proof-of-principle experimental setup to validate the H-G pointer theory and explore its potential applications in precision metrology.

中文翻译：

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用厄米-高斯指针进行高精度多参数弱测量

在理论和实验上，弱值放大技术都已被证明对精密计量有用。为了探索多参数估计的弱值放大的最终性能，我们借助高阶Hermite-Gaussian指针和量子Fisher信息矩阵，研究了一般的弱测量形式。理论分析表明，该方案的最终精度提高了2n + 1的平方根，其中n是Hermite-Gaussian模的阶数。而且，参数的估计精度可以通过最大似然估计法和零差法达到精度极限。我们还提供了原理验证实验设置，以验证HG指针理论并探索其在精密计量学中的潜在应用。