Optimal visible compression rate for mixed states is determined by entanglement of purification
Masahito Hayashi · Physical Review A · 2006
Entanglement of purification was introduced by Terhal et al. [J. Math. Phys. 43, 4286 (2002)] 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 [Phys. Rev. A61, 052309 (2000)] 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 unique interpretation to the entanglement of purification.