Nonadditivity of bipartite distillable entanglement follows from a conjecture on bound entangled Werner states

Assuming the validity of a conjecture given by DiVincenzo et al. [Phys. Rev . A 61, 062312 (2000)] and by Dur et al. [Phys. Rev. A 61, 062313 (2000)], we show that the distillable entanglement for two bipartite states, each of which individually has zero distillable entanglement, can be nonzero. We s how that this also implies that the distillable entanglement is not a conve x function. Our example consists of the tensor product of a bound entangled state based on an unextendible product basis with an entangled Werner stat e which lies in the class of conjectured undistillable states.