Mutual catalysis of entanglement transformations for pure entangled states

We study the mutual catalysis of entanglement transformations, which refers to the fact that each of the two entanglement transformations cannot occur with certainty by local operations and classical communication independently, but both can occur jointly if collective local operations are performed on both of the initial entangled states. We surprisingly find that mutually catalyzed transformations can be realized even in the case when the standard entanglement catalyzed transformations [D. Jonathan and M. B. Plenio, Phys. Rev. Lett. 83, 3566 (1999)] are forbidden.