Real-life applications like magnetometry or quantum gyroscope typically involve precise measurement on multiple parameters. How to achieve the ultimate precision limits simultaneously is a long sought-after grail in the field.
It is widely believed that the ultimate precision limits for all parameters cannot be achieved simultaneously, since generators of different parameters are generally non-commuting, which induces the trade-offs among the precisions.
Yet such trade-offs are escaped from by the group of Prof. LI Chuanfeng and Prof. XIANG Guoyong from Key Laboratory of Quantum Information at University of Science and Technology of China of the Chinese Academy of Sciences and their collaborator Prof. YUAN Haidong from Chinese University of Hongkong.
They counteracted the trade-offs and achieved the precision limit for the estimation of all three parameters in SU(2) operators simultaneously with 13.27 dB improvement over the shot-noise limit, which has been published in journal Science Advances.
XIANG and researchers extended the control-enhanced sequential measurement scheme from single-parameter estimation to multi-parameter estimation.
They related the simultaneous multi-parameter quantum estimation directly to the Heisenberg uncertainty relations and showed that to achieve the precision limit for multiple parameters simultaneously requires the simultaneous saturation of the minimum uncertainty in multiple Heisenberg uncertainty relations.
As the first experimental demonstration of multi-parameter quantum estimation with zero trade-off, the work reveals the deep connection between quantum metrology and the Heisenberg uncertainty principle and marks a crucial step towards achieving the ultimate precision of multi-parameter quantum estimation.
XIANG’s group have been dedicated to counteracting the trade-offs in multi-parameter estimation. They first developed new experimental measurement techniques of collective measurements, which successfully reduced the trade-offs in quantum state tomography and quantum orienteering . Then they optimized the entangled probe states in quantum magnetometry and obtained the ultimate precision limit for three magnetic components with minimum trade-offs. Though diminished, the trade-offs still exist in these past works.
Reference: “Zero–trade-off multiparameter quantum estimation via simultaneously saturating multiple Heisenberg uncertainty relations” by Zhibo Hou, Jun-Feng Tang, Hongzhen Chen, Haidong Yuan, Gou-Yong Xiang, Chuan-Feng Li and Guang-Can Guo, 1 January 2021, Science Advances.