Audenaert, K., De Moor, B., Vollbrecht, K-G. H. and Werner, R. F. (2002) Asymptotic Relative Entropy of Entanglement for Orthogonally Invariant States. Physical Review A, 66
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For a special class of bipartite states we calculate explicitly the asymptotic relative entropy of entanglement $E_R^\infty$ with respect to states having a positive partial transpose (PPT). This quantity is an upper bound to distillable entanglement. The states considered are invariant under rotations of the form $O\otimes O$, where $O$ is any orthogonal matrix. We show that in this case $E_R^\infty$ is equal to another upper bound on distillable entanglement, constructed by Rains. To perform these calculations, we have introduced a number of new results that are interesting in their own right: (i) the Rains bound is convex and continuous; (ii) under some weak assumption, the Rains bound is an upper bound to $E_R^\infty$; (iii) for states for which the relative entropy of entanglement $E_R$ is additive, the Rains bound is equal to$E_R$.
This is a Submitted version This version's date is: 24/4/2002 This item is not peer reviewed
https://repository.royalholloway.ac.uk/items/36eb5473-295a-43b4-de97-faf820af3436/6/
Deposited by Research Information System (atira) on 03-Jul-2014 in Royal Holloway Research Online.Last modified on 03-Jul-2014
11 pages, 5 figures