Bound on distillable entanglement

The best bound known on 2-locally distillable entanglement is that of Vedra l and Plenio, involving a certain measure of entanglement based on relative entropy. It turns out that a related argument can be used to give an even stronger bound; we give this bound, and examine some of its properties. In particular, and in contrast to the earlier bounds, the new bound is not add itive in general. We give an example of a state for which the bound fails t o be additive, as well as a number of states for which the bound is additiv e.