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We demonstrate the capability of continuous variable Gaussian states tocommunicate multipartite quantum information. A quantum teamwork protocol ispresented according to which an arbitrary possibly entangled multimode statecan be faithfully teleported between two teams each comprising many cooperativeusers. We prove that N-mode Gaussian weighted graph states exist for arbitraryN, that enable unconditional quantum teamwork implementations for anyarrangement of the teams. These perfect continuous variable maximallymultipartite entangled resources are typical among pure Gaussian states and areunaffected by the entanglement frustration occurring in multiqubit states.

Quantum Teamwork for Unconditional Multiparty Communication with Gaussian States