The estimation of parameters plays a central role in science and technology. It is based on measurements made on probe systems undergoing a parameter-dependent process. Quantum metrology deals with the ultimate precision limits in estimation procedures, taking into account the constraints imposed by quantum mechanics. The parameters of interest could be for instance a phase displacement in an optical interferometer, the time durations of a physical process, a tiny force acting on a mesoscopic object, or the frequency of an atomic transition. The estimation error decreases with the number N of resources employed in the measurement (number of probes, probe energy). Quantum mechanics imposes restrictions on the precision of the estimation, since two outgoing states corresponding to two different values of the parameter are not necessarily distinguishable, and furthermore measurements must conform to quantum constraints. On the other hand, quantum features, like entanglement and squeezing, help to increase the estimation accuracy beyond the standard limit, yielding better precision for the same amount of resources. However, the precision of recent experiments, while beginning to reach the limits imposed by quantum mechanics, is spoiled by the unavoidable influence of noise. Evaluating this effect is a difficult task. While exact results and analytical solutions are known for noiseless situations, the determination of the ultimate precision limit in the presence of noise is still a challenging problem in quantum mechanics. This talk will review some of the achievements and difficulties of quantum metrology, and will present a recently proposed method [1,2,3] that transforms the noisy evolution into a unitary one in an extended Hilbert space that describes both the system and the environment. This method is applied to obtain an exact solution for the precision limit in the measurement of a weak force acting a noisy harmonic oscillator , and very good bounds for the precision in optical interferometry and atomic spectroscopy [1,2], as well as for the quantum speed of physical processes .
Luiz Davidovich is Professor of Physics at the Federal University of Rio de Janeiro, director of the Brazilian Academy of Sciences, and member of the Board of the InterAcademy Council (IAC). He got his Ph. D. at the University of Rochester in 1975, and has worked since then in quantum optics and quantum information.
His major contributions are in the topics of decoherence, entanglement, laser theory, and quantum metrology. He has analyzed in detail the role of the environment in the dynamics of quantum coherence and quantum entanglement, and also in quantum metrology, contributing with theoretical developments and proposals for experiments, which have been performed in Europe and by his own group in Brazil.
He was elected as foreign associate to the National Academy of Sciences of the United States of America in 2006. In 2000, he was awarded the Brazilian Grand-Cross of the National Order of Scientific Merit. He won the 2001 Physics Prize of the Academy of Sciences for the Developing World (TWAS). He also won, in 2010, the most important prize for science in Brazil, the Admiral Alvaro Alberto prize, awarded by the Brazilian National Research Council. He is a fellow of the Optical Society of America.