Quantum non demolition measurements: parameter estimation for mixtures of multinomials

@article{Benoist2017QuantumND,
  title={Quantum non demolition measurements: parameter estimation for mixtures of multinomials},
  author={Tristan Benoist and Fabrice Gamboa and Cl{\'e}ment Pellegrini},
  journal={arXiv: Quantum Physics},
  year={2017}
}
In Quantum Non Demolition measurements, the sequence of observations is distributed as a mixture of multinomial random variables. Parameters of the dynamics are naturally encoded into this family of distributions. We show the local asymptotic mixed normality of the underlying statistical model and the consistency of the maximum likelihood estimator. Furthermore, we prove the asymptotic optimality of this estimator as it saturates the usual Cramer Rao bound. 
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