Ab initio phase estimation at the shot noise limit with on–off measurement

  • Kaimin Zheng
  • Huichao Xu
  • Aonan Zhang
  • Xinghai Ning
  • Lijian ZhangEmail author


Phase resolution at the shot noise limit can be achieved with coherent states and on–off measurement. However, the estimation of an unknown phase using this scheme is still missing. Here, we experimentally demonstrate an ab initio phase estimation at the shot noise limit using on–off measurement and efficient Bayesian inference algorithm. The performance of the schemes with and without real-time feedback control is compared. The scheme with feedback control eliminates the ambiguity in the phase estimation and accelerates the convergence to true value. The shot noise limit that defines the ultimate precision is saturated independent of the true phase after about 150 rounds of measurement and feedback control. Our protocol may find important applications in practical precision metrology when only a limited number of measurements are allowed.


Quantum metrology Cramér–Rao bound Shot noise limit On–off measurement Bayesian inference Real-time feedback 



This work was supported by the National Key Research and Development Program of China under Grant No. 2017YFA0303703, the National Natural Science Foundation of China under Grants Nos. 91536113, 11690032, 61490711, 11474159, 91836303, the Fundamental Research Funds for the Central Universities under Grant No. 021314380111, the Nanjing University Innovation and Creative Program for PhD candidate (2016017).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Kaimin Zheng
    • 1
    • 2
  • Huichao Xu
    • 1
    • 2
  • Aonan Zhang
    • 1
    • 2
  • Xinghai Ning
    • 1
    • 2
  • Lijian Zhang
    • 1
    • 2
    Email author
  1. 1.National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education), College of Engineering and Applied SciencesNanjing UniversityNanjingChina
  2. 2.Collaborative Innovation Center of Advanced MicrostructuresNanjing UniversityNanjingChina

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