Quantum non demolition measurements: parameter estimation for mixtures of multinomials

  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},
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. 
2 Citations

Figures from this paper

On asymptotic stability of quantum trajectories and their Cesaro mean
We address the question of asymptotic stability of quantum trajectories, also referred as quantum filters. We determine the limit of the quantum fidelity between the true quantum trajectory and theExpand
Perturbation Theory for Weak Measurements in Quantum Mechanics, Systems with Finite-Dimensional State Space
The quantum theory of indirect measurements in physical systems is studied. The example of an indirect measurement of an observable represented by a self-adjoint operator $${\mathcal {N}}$$N withExpand


Equivalence Classes and Local Asymptotic Normality in System Identification for Quantum Markov Chains
We consider the problem of identifying and estimating dynamical parameters of an ergodic quantum Markov chain, when only the stationary output is accessible for measurements. The starting point ofExpand
Repeated Quantum Non-Demolition Measurements: Convergence and Continuous Time Limit
We analyze general enough models of repeated indirect measurements in which a quantum system interacts repeatedly with randomly chosen probes on which von Neumann direct measurements are performed.Expand
Fisher informations and local asymptotic normality for continuous-time quantum Markov processes
We consider the problem of estimating an arbitrary dynamical parameter of an quantum open system in the input-output formalism. For irreducible Markov processes, we show that in the limit of largeExpand
Indirect Acquisition of Information in Quantum Mechanics
Long sequences of successive direct (projective) measurements or observations of just a few “uninteresting” physical quantities pertaining to a quantum system, such as clicks of some detectors, mayExpand
Parameter estimation from measurements along quantum trajectories
A new formulation of particle quantum filters is proposed to prove stability, and to provide an efficient algorithm preserving, for any discretization step-size, positivity of the quantum states and parameter classical probabilities. Expand
Convergence of repeated quantum nondemolition measurements and wave-function collapse
Motivated by recent experiments on quantum trapped fields, we give a rigorous proof that repeated indirect quantum nondemolition (QND) measurements converge to the collapse of the wave function asExpand
Iterated stochastic measurements
We describe a measurement device principle based on discrete iterations of Bayesian updating of system-state probability distributions. Although purely classical by nature, these measurements areExpand
Large Time Behavior and Convergence Rate for Quantum Filters Under Standard Non Demolition Conditions
A quantum system $${\mathcal S}$$S undergoing continuous time measurement is usually described by a jump-diffusion stochastic differential equation. Such an equation is called a quantum filteringExpand
Statistical structure of quantum theory
The course presents some basic concepts and rigorous results of a new scientiflc discipline { quantum information theory. It starts with a thorough reconsideration of the mathematical foundations ofExpand
Progressive field-state collapse and quantum non-demolition photon counting
The observation of such a step-by-step collapse by non-destructively measuring the photon number of a field stored in a cavity is reported, which illustrates all the postulates of quantum measurement (state collapse, statistical results and repeatability) and should facilitate studies of non-classical fields trapped in cavities. Expand