Multiparticle entanglement under asymptotic positive-partial-transpose-preserving operations

Abstract

We demonstrate that even under positive-partial-transpose-preserving operations in an asymptotic setting Greenberger-Horne-Zeilinger GHZ and W states are not reversibly interconvertible. We investigate the structure of minimal reversible entanglement generating set MREGS for tripartite states under positive-partialtranspose- PPT- preserving operations. We demonstrate that the set consisting of W and Einstein-PodolskyRosen EPR states alone cannot be an MREGS. In this context we prove the surprising result that the relative entropy of entanglement can be strictly subadditive for certain pure tripartite states which is crucial to keep open the possibility that the set of GHZ state and EPR states together constitute an MREGS under PPTpreserving operations.