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

Quantum Physics