Asymptotic Manipulations of Entanglement Can Exhibit Genuine Irreversibility

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Abstract
It is commonly believed that distillation of entanglement can be, in general, irreversible. Perhaps the strongest evidence is constituted by the existence of the bound entangled states. However, even a single example of state exhibiting this irreversibility has not been found so far. We show that for a family of states the process of distillation of entanglement is truly irreversible. These states have a nonzero amount of bound entanglement and, at most, a very small amount of free entanglement.