Universal quantum state merging

We determine the optimal entanglement rate of quantum state merging when assuming that the state is unknown except for its membership in a certain set of states. We find that merging is possible at the lowest rate allowed by the individual states. Additionally, we establish a lower bound for the classical cost of state merging under state uncertainty. To this end we give an elementary proof for the cost in case of a perfectly known state which makes no use of the “resource framework.” As applications of our main result, we determine the capacity for one-way entanglement distillation if the source is not perfectly known. Moreover, we give another achievability proof for the entanglement generation capacity over compound quantum channels.