  Antideuteron and antihelium nuclei have been proposed as promising detection
channels for dark matter because of the low astrophysical backgrounds expected.
To estimate both potential exotic contributions and their backgrounds, one
usually employs the coalescence model in momentum space. Here we use instead a
newly developed coalescence model based on the Wigner function representations
of the produced nuclei states. This approach includes both the
process-dependent size of the formation region of antinuclei, and the momentum
correlations of coalescing antinucleons in a semi-classical picture. The model
contains a single universal parameter $\sigma$ that we tune to experimental
data on antideuteron production in electron-positron, proton-proton and
proton-nucleus collisions. The obtained value $\sigma\simeq 1$ fm agrees well
with its physical interpretation as the size of the formation region of
antinuclei in collisions of point-like particles. This model allows us
therefore to calculate in a consistent frame-work the antideuteron and
antihelium fluxes both from secondary production and from dark matter
annihilations. We find that the antihelium-3 flux falls short by more than an
order of magnitude of the detection sensitivity of the AMS-02 experiment,
assuming standard cosmic ray propagation parameters, while the antideuteron
flux can be comparable to the sensitivities of the AMS-02 and GAPS experiments.
