  Photon addition and subtraction render Gaussian states non-Gaussian. We
provide a quantitative analysis of the change in nonclassicality produced by
these processes by analyzing the Wigner negativity and quadrature coherence
scale (QCS) of the resulting states. The QCS is a recently introduced measure
of nonclassicality [PRL 122, 080402 (2019), PRL 124, 090402 (2020)], that we
show to undergo a relative increase under photon addition/subtraction that can
be as large as 200\%. This implies that the degaussification and the
concomitant increase of nonclassicality come at a cost. Indeed, the QCS is
proportional to the decoherence rate of the state so that the resulting states
are considerably more prone to environmental decoherence. Our results are
quantitative and rely on explicit and general expressions for the
characteristic and Wigner functions of photon added/subtracted single- and
multi-mode Gaussian states for which we provide a simple and straightforward
derivation. These expressions further allow us to certify the quantum
non-Gaussianity of the photon-subtracted states with positive Wigner function.
