QUANTUM ESTIMATION DISCRIMINATION IN CONTINUOUS VARIABLE AND FERMIONIC SYSTEMS

In this PhD thesis we address the problem of characterizing quantum states and parameters of systems that are of particular interest for quantum technologies. In the first part we consider continuous variable systems and in particular Gaussian states; we address the estimation of quantities characterizing single-mode Gaussian states as the displacement and squeezing parameter and we study the improvement in the parameter estimation by introducing a Kerr nonlinearity. Moreover, we address the discrimination of noisy channels by means of Gaussian states as probe states considering two problems: the detection of a lossy channel against the alternative hypothesis of an ideal lossless channel and the discrimination of two Gaussian noisy channels. In the last part of the thesis, we consider the one dimensional quantum Ising model in a transverse magnetic field. We exploit the recent results about the geometric approach to quantum phase transitions to derive the optimal estimator of the coupling constant of the model at zero and finite temperature in both cases of few spins and in the thermodynamic limit. We also analyze the effects of temperature and the scaling properties of the estimator of the coupling constant. Finally, we consider the discrimination problem for two ground states or two thermal states of the model.