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We demonstrate that even under positive partial transpose preservingoperations in an asymptotic setting GHZ and W states are not reversiblyinterconvertible. We investigate the structure of minimal reversibleentanglement generating set (MREGS) for tri-partite states under positivepartial transpose (ppt) preserving operations. We demonstrate that the setconsisting of W and EPR states alone cannot be an MREGS. In this context weprove the surprising result that the relative entropy of entanglement can bestrictly sub-additive for certain pure tri-partite states which is crucial tokeep open the possibility that the set of GHZ-state and EPR states togetherconstitute an MREGS under ppt-preserving operations.Comment: Minor changes in the presentation, proof of strict sub-additivity of  relative entropy of entanglement for pure tri-partite states moved into main  text, results unchange

Publisher's Note: Multiparticle entanglement under asymptotic positive-partial-transpose-preserving operations [Phys. Rev.72, 042325 (2005)]