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

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

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.

Citation

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. https://doi.org/10.1088/1751-8113/48/36/365301

• 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
• DOI: https://doi.org/10.1088/1751-8113/48/36/365301
• Keywords: Quantum open systems, System identification, Quantum Markov processes, Quantum Fisher information, Local asymptotic normality, Continuous time measurements
• Public URL: https://nottingham-repository.worktribe.com/output/758832
• Publisher URL: https://doi.org/10.1088/1751-8113/48/36/365301
• Contract Date: Oct 9, 2017