Asymptotic relative entropy of entanglement for orthogonally invariant states
Abstract
For a special class of bipartite states we calculate explicitly the asymptotic relative entropy of entanglement E^{∞}_{R} 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 O⊗O, where O is any orthogonal matrix. We show that in this case E^{∞}_{R} 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} (iii) for states for which the relative entropy of entanglement E_{R} is additive, the Rains bound is equal to E_{R}.
 Publication:

Physical Review A
 Pub Date:
 September 2002
 DOI:
 10.1103/PhysRevA.66.032310
 arXiv:
 arXiv:quantph/0204143
 Bibcode:
 2002PhRvA..66c2310A
 Keywords:

 03.67.Hk;
 Quantum communication;
 Quantum Physics
 EPrint:
 11 pages, 5 figures