Zero-trade-off multiparameter quantum estimation via simultaneously saturating multiple Heisenberg uncertainty relations

Zhibo Hou; Jun-Feng Tang; Hongzhen Chen; Haidong Yuan; Guo-Yong Xiang; Chuan-Feng Li; Guang-Can Guo

doi:10.1126/sciadv.abd2986

Zero-trade-off multiparameter quantum estimation via simultaneously saturating multiple Heisenberg uncertainty relations

Sci Adv. 2021 Jan 1;7(1):eabd2986. doi: 10.1126/sciadv.abd2986. Print 2021 Jan.

Authors

Zhibo Hou^{1

2}, Jun-Feng Tang^{1

2}, Hongzhen Chen³, Haidong Yuan⁴, Guo-Yong Xiang^{5

2}, Chuan-Feng Li^{1

2}, Guang-Can Guo^{1

2}

Affiliations

¹ CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, P. R. China.
² CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, P. R. China.
³ Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong.
⁴ Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong. hdyuan@mae.cuhk.edu.hk gyxiang@ustc.edu.cn.
⁵ CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, P. R. China. hdyuan@mae.cuhk.edu.hk gyxiang@ustc.edu.cn.

Abstract

Quantum estimation of a single parameter has been studied extensively. Practical applications, however, typically involve multiple parameters, for which the ultimate precision is much less understood. Here, by relating the precision limit directly to the Heisenberg uncertainty relation, we show that to achieve the highest precisions for multiple parameters at the same time requires the saturation of multiple Heisenberg uncertainty relations simultaneously. Guided by this insight, we experimentally demonstrate an optimally controlled multipass scheme, which saturates three Heisenberg uncertainty relations simultaneously and achieves the highest precisions for the estimation of all three parameters in SU(2) operators. With eight controls, we achieve a 13.27-dB improvement in terms of the variance (6.63 dB for the SD) over the classical scheme with the same loss. As an experiment demonstrating the simultaneous achievement of the ultimate precisions for multiple parameters, our work marks an important step in multiparameter quantum metrology with wide implications.

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