Multiparticle entanglement under asymptotic positive-partial-transpose-preserving operations
Satoshi Ishizaka, Martin Bodo Plenio · Physical Review A · 2005
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-partial-transpose- (PPT-) preserving operations. We demonstrate that the set consisting of $W$ and Einstein-Podolsky-Rosen (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 PPT-preserving operations.