Statistical method for resolving the photon-photoelectron-counting inversion problem

  • Authors:

  • Jinlong Wu;Tiejun Li;Xiang Peng;Hong Guo

  • Affiliations:

  • LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, PR China;LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, PR China;CREAM Group, State Key Laboratory of Advanced Optical Communication Systems and Networks (Peking University) and Institute of Quantum Electronics, School of Electronics Engineering and Computer Sc ...;CREAM Group, State Key Laboratory of Advanced Optical Communication Systems and Networks (Peking University) and Institute of Quantum Electronics, School of Electronics Engineering and Computer Sc ...

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2011

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Abstract

A statistical inversion method is proposed for the photon-photoelectron-counting statistics in quantum key distribution experiment. With the statistical viewpoint, this problem is equivalent to the parameter estimation for an infinite binomial mixture model. The coarse-graining idea and Bayesian methods are applied to deal with this ill-posed problem, which is a good simple example to show the successful application of the statistical methods to the inverse problem. Numerical results show the applicability of the proposed strategy. The coarse-graining idea for the infinite mixture models should be general to be used in the future.