  Given a set of multipartite entangled states, can we find a common state to
prepare them by local operations and classical communication? Such a state, if
exists, will be a common resource for the given set of states. We completely
solve this problem for bipartite pure states case by explicitly constructing a
unique optimal common resource state for any given set of states. In the
multipartite setting, the general problem becomes quite complicated, and we
focus on finding nontrivial common resources for the whole multipartite state
space of given dimensions. We show that GHZ_3 is a nontrivial common resource
for three-qubit systems.
