Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics

Gu??, M?d?lin; Kiukas, Jukka

Abstract

This paper deals with the problem of identifying and estimating dynamical parameters of continuous-time Markovian quantum open systems, in the input-output formalism. First, we characterise the space of identifiable parameters for ergodic dynamics, assuming full access to the output state for arbitrarily long times, and show that the equivalence classes of undistinguishable parameters are orbits of a Lie group acting on the space of dynamical parameters. Second, we define an information geometric structure on this space, including a principal bundle given by the action of the group, as well as a compatible connection, and a Riemannian metric based on the quantum Fisher information of the output. We compute the metric explicitly in terms of the Markov covariance of certain "fluctuation operators", and relate it to the horizontal bundle of the connection. Third, we show that the system-output and reduced output state satisfy local asymptotic normality, i.e. they can be approximated by a Gaussian model consisting of coherent states of a multimode continuos variables system constructed from the Markov covariance “data". We illustrate the result by working out the details of the information geometry of a physically relevant two-level system.

Citation

Gu??, M., & Kiukas, J. (in press). Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics. Journal of Mathematical Physics, 58, https://doi.org/10.1063/1.4982958

• Journal Article Type: Article
• Acceptance Date: Apr 24, 2017
• Online Publication Date: May 15, 2017
• Deposit Date: Apr 26, 2017
• Publicly Available Date: May 15, 2017
• Journal: Journal of Mathematical Physics
• Print ISSN: 0022-2488
• Electronic ISSN: 1089-7658
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 58
• DOI: https://doi.org/10.1063/1.4982958
• Public URL: https://nottingham-repository.worktribe.com/output/860756
• Publisher URL: http://aip.scitation.org/doi/10.1063/1.4982958
• Additional Information: The following article appeared in Journal of Mathematical Physics and may be found at http://aip.scitation.org/doi/10.1063/1.4982958 This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.; ; The following article has been accepted by Journal of Mathematical Physics. After it is published, it will be found at http://aip.scitation.org/journal/jmp.