Irreversibility in asymptotic manipulations of a distillable entangled state

We provide an example of a distillable bipartite mixed state such that, even in the asymptotic limit, more pure-state entanglement is required to create it than can be distilled from it. Thus, we show that the irreversibility in the processes of formation and distillation of bipartite states, recently proved in [G. Vidal and J. I. Cirac, Phys. Rev. Lett. 86, 5803 (2001)], is not limited to bound-entangled states.