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This paper deals with the problem of identifying and estimating dynamicalparameters of continuous-time quantum open systems, in the input-outputformalism. First, we characterise the space of identifiable parameters forergodic dynamics, assuming full access to the output state for arbitrarily longtimes, and show that the equivalence classes of undistinguishable parametersare orbits of a Lie group acting on the space of dynamical parameters. Second,we define an information geometric structure on this space, including aprincipal bundle given by the action of the group, as well as a compatibleconnection, and a Riemannian metric based on the quantum Fisher information ofthe output. We compute the metric explicitly in terms of the Markov covarianceof certain "fluctuation operators", and relate it to the horizontal bundle ofthe connection. Third, we show that the system-output and reduced output statesatisfy local asymptotic normality, i.e. they can be approximated by a Gaussianmodel consisting of coherent states of a multimode continuos variables systemconstructed from the Markov covariance "data". We illustrate the result byworking out the details of the information geometry of a physically relevanttwo-level system.

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