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

Catana, Catalin; Bouten, Luc; Gu??, M?d?lin


Catalin Catana

Luc Bouten


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.


Catana, C., Bouten, L., & Guţă, M. (2015). Fisher informations and local asymptotic normality for continuous-time quantum Markov processes. Journal of Physics A: Mathematical and Theoretical, 48(36), Article 365301.

Journal Article Type Article
Acceptance Date Jul 21, 2015
Publication Date Aug 17, 2015
Deposit Date Oct 9, 2017
Journal Journal of Physics A: Mathematical and Theoretical
Print ISSN 1751-8113
Electronic ISSN 1751-8121
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 48
Issue 36
Article Number 365301
Keywords Quantum open systems, System identification, Quantum Markov processes, Quantum Fisher information, Local asymptotic normality, Continuous time measurements
Public URL
Publisher URL
Contract Date Oct 9, 2017