  We prove propagation of chaos at explicit polynomial rates in Wasserstein
distance W_2 for Kac's N-particle system associated with the spatially
homogeneous Boltzmann equation for Maxwell molecules, with and without cutoff.
Our approach is mainly based on novel probabilistic coupling techniques.
Combining them with recent stabilization results for the particle system we
obtain, under suitable moments assumptions on the initial distribution, a
uniform-in-time estimate of order almost N^{-1/3} for W_2^2.
