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Quantum non demolition measurements: parameter estimation for mixtures of multinomials. (English) Zbl 1388.81018

Summary: 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 Cramér Rao bound.

MSC:

81P15 Quantum measurement theory, state operations, state preparations
62F12 Asymptotic properties of parametric estimators
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References:

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