  We study completely positive and trace-preserving equivariant maps between
operators on irreducible representations of $\mathrm{SU}(2)$. We find
asymptotic approximations of channels in the limit of large output
representation and we compute traces of functions of channel outputs. Our main
tool is quantization using coherent states. We provide quantitative error
bounds for various semiclassical formulas satisfied by quantizations of
functions on the sphere.
