Parton showers with quantum interference: leading color, with spin
  We have previously described a mathematical formulation for a parton shower based on the approximation of strongly ordered virtualities of successive parton splittings. Quantum interference, including interference among different color and spin states, was included. A practical numerical implementation strategy was left unspecified. In a subsequent paper, we showed that if we add the further approximations of taking only the leading color limit and averaging over spins, we obtain a shower evolution that can be implemented as a Markov process. In this paper, we outline a strategy for including the correlations induced by parton spins. 
Zoltan Nagy and Davison E. Soper