We consider the problem of estimating an arbitrary dynamical parameter of an quantum open 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 $t^{-1/2}$ 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 mathematical theorems are 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.
We describe how to characterize dynamical phase transitions in open quantum systems from a purely dynamical perspective, namely, through the statistical behavior of quantum jump trajectories. This approach goes beyond considering only properties of t
he steady state. While in small quantum systems dynamical transitions can only occur trivially at limiting values of the controlling parameters, in many-body systems they arise as collective phenomena and within this perspective they are reminiscent of thermodynamic phase transitions. We illustrate this in open models of increasing complexity: a three-level system, a dissipative version of the quantum Ising model, and the micromaser. In these examples dynamical transitions are accompanied by clear changes in static behavior. This is however not always the case, and in general dynamical phase behavior needs to be uncovered by observables which are strictly dynamical, e.g. dynamical counting fields. We demonstrate this via the example of a class of models of dissipative quantum glasses, whose dynamics can vary widely despite having identical (and trivial) stationary states.
We provide efficient and intuitive tools for deriving bounds on achievable precision in quantum enhanced metrology based on the geometry of quantum channels and semi-definite programming. We show that when decoherence is taken into account, the maxim
al possible quantum enhancement amounts generically to a constant factor rather than quadratic improvement. We apply these tools to derive bounds for models of decoherence relevant for metrological applications including: dephasing,depolarization, spontaneous emission and photon loss.
