We propose schemes to perform the deterministic dense coding and faithful teleportation with multipartite graph states. We also find the sufficient and necessary condition of a viable graph state for the proposed schemes. That is, for the associated graph, the reduced adjacency matrix of the Tanner-type subgraph between senders and receivers should be invertible.

• Received 3 July 2008

DOI:https://doi.org/10.1103/PhysRevA.79.052306