This paper is concerned with the estimation of dynamical parameters of an open quantum system in the input-output formalism. In particular, it is shown that the joint system-output state converges in large time to a quantum Gaussian state whose mean can be used to estimate the unknown parameter. In addition, an explicit asymptotic expression is given for the quantum Fisher information of the model, which provides an upper bound on the precision of the estimation. Local asymptotic normality is also established for counting and homodyne measurements performed on the system output, together with expressions for their classical Fisher information. The examples considered include a two-level system and the atom maser.
This extends to continuous-time open quantum systems the asymptotic normality results derived in [the third author et al., “Fisher information and asymptotic normality in system identification for quantum Markov chains”, Phys. Rev. A 83, No. 6, Article ID 062324, 9 p. (2011; doi:10.1103/PhysRevA.83.062324); Commun. Math. Phys. 335, No. 3, 1397–1428 (2015; Zbl 1319.81017)], for discrete-time quantum Markov chains. The extension relies on quantum stochastic calculus.