Multipartite purification protocols: upper and optimal bounds
  A method for producing an upper bound for all multipartite purification protocols is devised, based on knowing the optimal protocol for purifying bipartite states. When applied to a range of noise models, both local and correlated, the optimality of certain protocols can be demonstrated for a variety of graph and valence bond states. 
Alastair Kay and Jiannis K. Pachos