Exact Results in Quantum Theory

Quantum metrology investigates the possibility of exploiting quantum features such as coherence and entanglement to boost the precision of measurements of time, length etc.From a more mathematical perspective it is a theory on the optimal strategies in discriminating quantum channels. I will give a brief review of the most interesting result from the field and connect abstract concepts such as geometry of completely-positive maps and the quantum Master equation with real life problems such as fundamental limits to stability of atomic clocks and sensitivity of gravitational wave detectors.