  The quadrature coherence scale (QCS) is a recently introduced measure that
was shown to be an efficient witness of nonclassicality. It takes a simple form
for pure and Gaussian states, but a general expression for mixed states tends
to be prohibitively unwieldy. In this paper, we introduce a method for
computing the quadrature coherence scale of quantum states characterized by
Wigner functions expressible as linear combinations of Gaussian functions.
Notable examples within this framework include cat states, GKP states, and
states resulting from Gaussian transformations, measurements, and breeding
protocols. In particular, we show that the quadrature coherence scale serves as
a valuable tool for examining the scalability of nonclassicality in the
presence of loss. Our findings lead us to put forth a conjecture suggesting
that, subject to 50% loss or more, all pure states lose any QCS-certifiable
nonclassicality. We also consider the quadrature coherence scale as a measure
of quality of the output state of the breeding protocol.
