  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
$E_R$.
