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Multimode Gaussian quantum light, which includes multimode squeezed andmultipartite quadrature entangled light, is a very general and powerful quantumresource with promising applications in quantum information processing andmetrology. In this paper, we determine the ultimate sensitivity in theestimation of any parameter when the information about this parameter isencoded in such light, irrespective of the information extraction protocol usedin the estimation and of the measured observable. In addition we show that anappropriate homodyne detection scheme allows us to reach this ultimatesensitivity. We show that, for a given set of available quantum resources, themost economical way to maximize the sensitivity is to put the most squeezedstate available in a well-de ned light mode. This implies that it is notpossible to take advantage of the existence of squeezed fluctuations in othermodes, nor of quantum correlations and entanglement between diff erent modes.

Ultimate sensitivity of precision measurements with Gaussian quantum light : a multi-modal approach