  Entanglement of purification was introduced by Terhal et al. for
characterizing the bound of the generation of correlated states from maximally
entangled states with sublinear size of classical communication. On the other
hand, M. Horodecki obtained the optimal compression rate with a mixed states
ensemble in the visible setting. In this paper, we prove that the optimal
visible compression rate for mixed states is equal to the limit of the
regularized entanglement of purification of the state corresponding to the
given ensemble. This result gives a new interpretation to the entanglement of
purification.
