Hou Zhibo, Zhang Zhao, Xiang Guo-Yong, Li Chuan-Feng, Guo Guang-Can, Chen Hongzhen, Liu Liqiang, Yuan Haidong
CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China.
Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong.
Phys Rev Lett. 2020 Jul 10;125(2):020501. doi: 10.1103/PhysRevLett.125.020501.
The precise measurement of a magnetic field is one of the most fundamental and important tasks in quantum metrology. Although extensive studies on quantum magnetometry have been carried out over past decades, the ultimate precision that can be achieved for the estimation of all three components of a magnetic field under the parallel scheme remains unknown. This is largely due to the lack of understandings on the incompatibility of the optimal probe states for the estimation of the three components. Here we provide an approach to characterize the minimal tradeoff among the precisions of multiple parameters that arise from the incompatibility of the optimal probe states, which leads to the identification of the ultimate precision limit for the estimation of all three components of a magnetic field under the parallel scheme. The optimal probe state that achieves the ultimate precision is also explicitly constructed. The obtained precision sets a benchmark on the precision of the multiparameter quantum magnetometry under the parallel scheme, which is of fundamental interest and importance in quantum metrology.
磁场的精确测量是量子计量学中最基本且重要的任务之一。尽管在过去几十年里已经对量子磁强计进行了广泛研究，但在平行方案下估计磁场所有三个分量时能够达到的最终精度仍然未知。这主要是由于对用于估计三个分量的最优探测态的不相容性缺乏理解。在此，我们提供一种方法来表征由最优探测态的不相容性所导致的多个参数精度之间的最小权衡，这使得我们能够确定平行方案下磁场所有三个分量估计的最终精度极限。还明确构造了达到最终精度的最优探测态。所获得的精度为平行方案下多参数量子磁强计的精度设定了一个基准，这在量子计量学中具有根本的重要性。
