Quantum non demolition measurements: parameter estimation for mixtures of multinomials

TL;DR

This paper investigates quantum non-demolition measurements where observations follow a mixture of multinomials, establishing the statistical properties and optimality of parameter estimation methods within this framework.

Contribution

It demonstrates the local asymptotic mixed normality and consistency of the maximum likelihood estimator, proving its asymptotic optimality in quantum measurement models.

Findings

Establishes local asymptotic mixed normality of the model

Proves consistency of the maximum likelihood estimator

Shows the estimator saturates the Cramér-Rao bound

Abstract

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 Cram\'er Rao bound.