Asymptotic relative entropy of entanglement for orthogonally invariant states
K. Audenaert, Bart De Moor, K. G. H. Vollbrecht +1 more
For a special class of bipartite states we calculate explicitly the asymptotic relative entropy of entanglement ${E}_{R}^{\ensuremath{\infty}}$ with respect to states having a positive partial transpose. This quantity is an upper bound to distillable entanglement. The states considered are invariant under rotations of the form $\mathrm{O}\ensuremath{\bigotimes}\mathrm{O},$ where O is any orthogonal matrix. We show that in this case ${E}_{R}^{\ensuremath{\infty}}$ is equal to another upper bound on distillable entanglement, constructed by Rains. To perform these calculations, we have introduced a number of 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 ${E}_{R}^{\ensuremath{\infty}};$ (iii) for states for which the relative entropy of entanglement ${E}_{R}$ is additive, the Rains bound is equal to ${E}_{R}.$
arXiv:quant-ph/0204143•Physical Review A•Sep 18, 2002•83 citations