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Multi-particle entanglement under asymptotic positive partial transpose preserving operations

S. Ishizaka·M. B. Plenio
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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.

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S. Ishizaka, M. B. Plenio. 2005-05-26. Multi-particle entanglement under asymptotic positive partial transpose preserving operations. https://doi.org/10.1103/physreva.72.059907

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