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

Guţă, Mădălin; Kiukas, Jukka

Authors

Jukka Kiukas



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

Guţă, 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 AIP Publishing
Peer Reviewed Peer Reviewed
Volume 58
DOI https://doi.org/10.1063/1.4982958
Public URL http://eprints.nottingham.ac.uk/id/eprint/42291
Publisher URL http://aip.scitation.org/doi/10.1063/1.4982958
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf
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.

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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