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In the context of phase estimation with Gaussian states, we introduce aquantifiable definition of metrological advantage that takes into accountthermal noise in the preparation procedure. For a broad set of states,\textit{isotropic non-pure Gaussian states}, we show that squeezing is not onlynecessary, but sufficient, to achieve metrological advantage. We interpret ourresults in the framework of resource theory, and discuss possible sources ofadvantage other than squeezing. Our work is a step towards using phaseestimation with pure and mixed state to define and quantify nonclassicality.This work is complementary with studies that defines nonclassicality usingquadrature displacement estimation.

Metrological advantage at finite temperature for Gaussian phase estimation