We address the problem of the optimal quantum estimation of the coupling parameter of a bilinear interaction, such as the transmittivity of a beam splitter or the internal phase-shift of an interferometer. The optimal measurement scheme exhibits Heisenberg scaling of the measurement precision versus the total energy.
@article{arxiv.quant-ph/0103080,
title = {Optimal quantum estimation of the coupling between two bosonic modes},
author = {G. Mauro D'Ariano and Matteo G. A. Paris and Paolo Perinotti},
journal= {arXiv preprint arXiv:quant-ph/0103080},
year = {2007}
}