Zhang Yong-Liang, Wang Huan, Jing Li, Mu Liang-Zhu, Fan Heng
School of Physics, Peking University, Beijing 100871, China.
School of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China.
Sci Rep. 2014 Dec 9;4:7390. doi: 10.1038/srep07390.
The linear function is possibly the simplest and the most used relation appearing in various areas of our world. A linear relation can be generally determined by the least square linear fitting (LSLF) method using several measured quantities depending on variables. This happens for such as detecting the gradient of a magnetic field. Here, we propose a quantum fitting scheme to estimate the magnetic field gradient with N-atom spins preparing in W state. Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cramér-Rao bound (QCRB). We show that the estimated quantity achieves the Heisenberg-scaling accuracy. Our scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.
线性函数可能是出现在我们世界各个领域中最简单且使用最广泛的关系。线性关系通常可以通过最小二乘线性拟合（LSLF）方法，利用几个依赖于变量的测量量来确定。例如在检测磁场梯度时就是这种情况。在此，我们提出一种量子拟合方案，用于利用制备在W态的N个原子自旋来估计磁场梯度。我们的方案将量子多参数估计与最小二乘线性拟合方法相结合，以达到量子克莱姆 - 拉奥界（QCRB）。我们表明，估计量实现了海森堡标度精度。我们的量子计量方案与数据拟合相结合，为快速高精度测量提供了一种新方法。
