On the structure of a reversible entanglement generating set for tripartite states

We show that Einstein-Podolsky-Rosen-Bohm (EPR) and Greenberger-Horne-Zeilinger-Mermin (GHZ) states can not generate, through local manipulation and in the asymptotic limit, all forms of tripartite pure-state entanglement in a reversible way. The techniques that we use indicate that there is a connection between this result and the irreversibility that occurs in the asymptotic preparation and distillation of bipartite mixed states.