Quantum metrology - from fundamentals to applications

Quantum metrology is the theory of parameter estimation in quantum systems. To achieve precision improvements beyond classical limits, we prepare quantum states with low quantum fluctuations and we measure observables that carry maximal information about the parameter of interest. The advances in experimental systems over the past decades allow us today to implement these ideas, e.g., in cold-atom laboratories or in quantum optics. In this seminar we will present an introduction to the theory of quantum metrology, Fisher information and its Gaussian (spin squeezing) and non-Gaussian approximations. Moverover, we are going to discuss the relation between quantum metrology and information theory, especially the role played by entanglement in precision measurements. Finally, we will see some applications of this theory in atomic interferometers and in quantum superresolution imaging.