1 College of Physical Science and Technology, Sichuan University, Chengdu 610064, China;
2 Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University, Chengdu 610064, China;
3 Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 400714, China
Pre- and post-selected (PPS) measurement, especially the weak PPS measurement, has been proved to be a useful tool for measuring extremely tiny physical parameters. However, it is difficult to retain both the attainable highest measurement sensitivity and precision with the increase of the parameter to be measured. Here, a modulated PPS measurement scheme based on coupling-strength-dependent modulation is presented with the highest sensitivity and precision retained for an arbitrary coupling strength. This idea is demonstrated by comparing the modulated PPS measurement scheme with the standard PPS measurement scheme in the case of unbalanced input meter. By using the Fisher information metric, we derive the optimal pre- and post-selected states, as well as the optimal coupling-strength-dependent modulation without any restriction on the coupling strength. We also give the specific strategy of performing the modulated PPS measurement scheme, which may promote practical application of this scheme in precision metrology.
Project supported by the National Natural Science Foundation of China (Grant Nos. 11674234 and 11605205), the Fundamental Research Funds for the Central Universities, China (Grant No. 2012017yjsy143), the National Key Research and Development Program of China (Grant No. 2017YFA0305200), the Youth Innovation Promotion Association of Chinese Academy of Sciences (CAS) (Grant No. 2015317), the Natural Science Foundation of Chongqing, China (Grant Nos. cstc2015jcyjA00021 and cstc2018jcyjAX0656), the Entrepreneurship and Innovation Support Program for Chongqing Overseas Returnees, China (Grant No. cx017134), the Fund of CAS Key Laboratory of Microscale Magnetic Resonance, China, and the Fund of CAS Key Laboratory of Quantum Information, China.
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