  The addition or subtraction of a photon from a Gaussian state of light is a
versatile and experimentally feasible procedure to create non-Gaussian states.
In multimode setups, these states manifest a wide range of phenomena when the
photon is added or subtracted in a mode-tunable way. In this contribution, we
derive the truncated correlations, which are multimode generalisations of
cumulants, between quadratures in different modes as statistical signatures of
these states. These correlations are then used to obtain the full multimode
Wigner function, the properties of which are subsequently studied. In
particular we investigate the effect of impurity in the subtraction or addition
process, and evaluate its impact on the negativity of the Wigner function.
Finally, we elaborate on the generation of inherent entanglement through
subtraction or addition of a photon from a pure squeezed vacuum.
