Resumo: The estimation of parameters characterizing dynamical processes is a central problem in science and technology. It concerns for instance the evaluation of the duration of some interaction or yet the phase shift in an interferometric measurement, due to the presence of gravitational waves. Since realistic experimental data have statistical uncertainties, due to external perturbations and/or intrinsic (quantum) fluctuations, it is not possible to univocally associate an experimental result (through an estimation) with the true value of the parameter. The uncertainty in estimation may be quantified by the square root of the statistical average of the square of the difference between the estimated and the true value of the parameter. The so-called Cramér–Rao limit yields a lower bound to this uncertainty. In single-parameter estimation, this bound is expressed in terms of a quantity known as Fisher Information. Quantum Metrology also deals with parameter estimation but takes into account the quantum character of the systems and processes involved. The so-called Quantum Fisher Information characterizes the maximum amount of information that can be extracted from quantum experiments about an unknown parameter using the best (and ideal) measurement device. It can be shown then that quantum strategies, involving non-classical characteristics of the probes, like entanglement and squeezing, lead to much better bounds, as compared with standard approaches that do not profit from these properties, in ideal-isolated systems. However, systems cannot be completely isolated from their environments. This leads to external fluctuations and the phenomenon of decoherence, which counteracts quantum effects, thus limiting the usefulness of quantum strategies. Earlier recipes for assessing the effect of noise on quantum-enhanced estimation were mathematically satisfactory but with little practical utility. In this talk I will present a new and general framework [1,2] for obtaining attainable and useful lower bounds for the estimation uncertainty in these more realistic systems, showing that the effectiveness of quantum states for parameter estimation in the presence of noise can be precisely assessed. As a concrete example, I will use this approach to delimiting the uncertainty limits on the estimation of phase-shifts in interferometers in the presence of phase-diffusion.
 B. M. Escher, R. L. de Matos Filho, and L. Davidovich, “General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology”, Nature Physics 7, 406-411 (2011);  B. M. Escher, R. L. de Matos Filho, and L. Davidovich,“Quantum Metrology for Noisy Systems”, Braz. J. Phys. 41, 229-247 (2011).