Cosine-of-phase sensitivity of a Mach-Zehnder interferometer for the Fock state inputs

In the case of the Mach-Zehnder interferometer fed with Fock states we speak of estimation of the cosine of phase instead of estimation of the phase. In case the numbers of input photons are equal, we pay attention to a proposal by Kim, et al. (1998). Then we restrict ourselves to the estimation of the cosine of double phase. Although such restrictions can be lifted, they harbinger a unified approach both to the phase sensitivity and to the Cramer-Rao lower bound of the estimator variance