title: Fitting magnetic field gradient with Heisenberg-scaling accuracy.
abstract: 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.
authors.affiliation: School of Physics, Peking University, Beijing 100871, China.
authors.forename: Yong-Liang
authors.initials: YL
authors.lastname: Zhang
authors.affiliation: School of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China.
authors.forename: Huan
authors.initials: H
authors.lastname: Wang
authors.affiliation: School of Physics, Peking University, Beijing 100871, China.
authors.forename: Li
authors.initials: L
authors.lastname: Jing
authors.affiliation: School of Physics, Peking University, Beijing 100871, China.
authors.forename: Liang-Zhu
authors.initials: LZ
authors.lastname: Mu
authors.affiliation: 1] Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China [2] Collaborative Innovation Center of Quantum Matter, Beijing 100190, China.
authors.forename: Heng
authors.initials: H
authors.lastname: Fan