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.