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Given a set of multipartite entangled states, can we find a common state toprepare them by local operations and classical communication? Such a state, ifexists, will be a common resource for the given set of states. We completelysolve this problem for bipartite pure states case by explicitly constructing aunique optimal common resource state for any given set of states. In themultipartite setting, the general problem becomes quite complicated, and wefocus on finding nontrivial common resources for the whole multipartite statespace of given dimensions. We show that GHZ_3 is a nontrivial common resourcefor three-qubit systems.

Common Resource State for Preparing Multipartite Quantum Systems via Local Operations and Classical Communication