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arXiv · 1401.5188

Fitting magnetic field gradient with Heisenberg-scaling accuracy

Yong-Liang Zhang·Huan Wang·Li Jing·Liang-Zhu Mu·Heng Fan
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Abstract

We propose a quantum fitting scheme to estimate the magnetic field gradient with $N$-atom spins preparing in W state, which attains the Heisenberg-scaling accuracy. 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. In single parameter estimation with assumption that the magnetic field is strictly linear, two optimal measurements can achieve the identical Heisenberg-scaling accuracy. Proper interpretation of the super-Heisenberg-scaling accuracy is presented. The scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.

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Yong-Liang Zhang, Huan Wang, Li Jing, Liang-Zhu Mu, Heng Fan. 2014-01-21. Fitting magnetic field gradient with Heisenberg-scaling accuracy. https://doi.org/10.1038/srep07390

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