Quantifying quantum-amplified metrology via Fisher information

We present a unified framework, based on quantum metrology concepts, for defining and quantifying deterministic noiseless quantum amplification of parameter-dependent processes, which plays an important role in increasing the precision of quantum sensing. Recent experiments [Burd et al., Science 364, 1163 (2019)] can be encompassed by this concept, which also leads to new suggestions of experimental work. The unified view presented here allows the identification of the basic steps for quantum amplification and of the measurements that lead to the best possible precision, beyond the quantum standard limit, in the estimation of parameters involved in the process. This is applied to the estimation of displacements of trapped ions and of the phase in SU(1,1) optical interferometers and atomic interferometry.