Optimized interferometry with Gaussian states

We revisit Mach-Zehnder interferometry using a suitable phase-space analysis and present a rigorous optimization of the sensitivity in realistic condition, i.e., for Gaussian input states, and taking into account nonunit quantum efficiency in the detection stage. The working regime of the interferometer is optimized at fixed input energy versus the squeezing phases and amplitudes as well as the distribution of squeezing in the two input signals. For ideal detection we find the known result that the squeezing resource allows to beat the shot-noise limit. For nonunit detection efficiency, we show that for fixed input energy one can always optimize the squeezing fraction in order to enhance the sensitivity with respect to the case of no squeezing, even in cases when one cannot go beyond the shot-noise limit