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Chin. Phys. B, 2021, Vol. 30(6): 064216    DOI: 10.1088/1674-1056/abcfa0

Parameter accuracy analysis of weak-value amplification process in the presence of noise

Jiangdong Qiu(邱疆冬)1, Zhaoxue Li(李兆雪)1, Linguo Xie(谢林果)2, Lan Luo(罗兰)1, Yu He(何宇)1, Changliang Ren(任昌亮)3,†, Zhiyou Zhang(张志友)1,‡, and Jinglei Du(杜惊雷)1
1 College of Physics, Sichuan University, Chengdu 610064, China;
2 Key Laboratory of Photonic and Optical Detection in Civil Aviation and Atmospheric Lidar Institute, Civil Aviation Flight University of China, Guanghan 618300, China;
3 Center for Nanofabrication and System Integration, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 400714, China
Abstract  We theoretically introduce the statistical uncertainty of photon number and phase error to discuss the precision of parameters to be measured based on weak measurements. When the photon counting scheme is used, we discuss the relative accuracy of the system in the presence of phase error by using the orthogonal and nonorthogonal pre- and post-selected states, respectively. When using the measurement scheme of pointer shift, we discuss the measurement accuracy in the presence of phase error, pointer resolution, and statistical uncertainty. These results give a guide way to get the smallest relative precision and deepen our understanding about weak measurement.
Keywords:  weak measurement      quantum measurement      accuracy analysis  
Received:  03 November 2020      Revised:  25 November 2020      Accepted manuscript online:  02 December 2020
PACS:  42.50.Tx (Optical angular momentum and its quantum aspects)  
  03.65.Ta (Foundations of quantum mechanics; measurement theory)  
  42.50.Xa (Optical tests of quantum theory)  
Fund: Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0305200), the National Natural Science Foundation of China (Grant Nos. 11674234 and 11605205), the Natural Science Foundation of Chongqing (Grant Nos. cstc2015jcyjA00021 and cstc2018jcyjAX0656), the Innovation Project of Sichuan University (Grant No. 2018SCUH0021), the Youth Innovation Promotion Association Program of the Chinese Academy of Sciences (CAS) (Grant No. No. 2015317), the Entrepreneurship and Innovation Support Program for Chongqing Overseas Returnees (Grant Nos. cx2017134 and cx2018040), the Fund of CAS Key Laboratory of Microscale Magnetic Resonance, and the Fund of CAS Key Laboratory of Quantum Information.
Corresponding Authors:  Changliang Ren, Zhiyou Zhang     E-mail:;

Cite this article: 

Jiangdong Qiu(邱疆冬), Zhaoxue Li(李兆雪), Linguo Xie(谢林果), Lan Luo(罗兰), Yu He(何宇), Changliang Ren(任昌亮), Zhiyou Zhang(张志友), and Jinglei Du(杜惊雷) Parameter accuracy analysis of weak-value amplification process in the presence of noise 2021 Chin. Phys. B 30 064216

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