Multi-particle entanglement under asymptotic positive partial transpose preserving operations
Abstract
We demonstrate that even under positive partial transpose preserving operations in an asymptotic setting GHZ and W states are not reversibly interconvertible. We investigate the structure of minimal reversible entanglement generating set (MREGS) for tri-partite states under positive partial transpose (ppt) preserving operations. We demonstrate that the set consisting of W and EPR states alone cannot be an MREGS. In this context we prove the surprising result that the relative entropy of entanglement can be strictly sub-additive for certain pure tri-partite 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.
Cite
@article{arxiv.quant-ph/0503025,
title = {Multi-particle entanglement under asymptotic positive partial transpose preserving operations},
author = {S. Ishizaka and M. B. Plenio},
journal= {arXiv preprint arXiv:quant-ph/0503025},
year = {2009}
}
Comments
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 unchanged