Fisher informations and local asymptotic normality for continuous-time quantum Markov processes

Catana, Catalin and Bouten, Luc and Guţă, Mădălin (2015) Fisher informations and local asymptotic normality for continuous-time quantum Markov processes. Journal of Physics A: Mathematical and Theoretical, 48 (36). 365301/1-365301/27. ISSN 1751-8121

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Abstract

We consider the problem of estimating an arbitrary dynamical parameter of an open quantum system in the input–output formalism. For irreducible Markov processes, we show that in the limit of large times the system-output state can be approximated by a quantum Gaussian state whose mean is proportional to the unknown parameter. This approximation holds locally in a neighbourhood of size in the parameter space, and provides an explicit expression of the asymptotic quantum Fisher information in terms of the Markov generator. Furthermore we show that additive statistics of the counting and homodyne measurements also satisfy local asymptotic normality and we compute the corresponding classical Fisher informations. The general theory is illustrated with the examples of a two-level system and the atom maser. Our results contribute towards a better understanding of the statistical and probabilistic properties of the output process, with relevance for quantum control engineering, and the theory of non-equilibrium quantum open systems.

Item Type: Article
Keywords: Quantum open systems, System identification, Quantum Markov processes, Quantum Fisher information, Local asymptotic normality, Continuous time measurements
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1088/1751-8113/48/36/365301
Depositing User: Eprints, Support
Date Deposited: 09 Oct 2017 12:14
Last Modified: 13 Oct 2017 03:25
URI: http://eprints.nottingham.ac.uk/id/eprint/47093

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