Abstract
We present a universal protocol for continuous-variable graph-state teleportation. A mathematical model is established to determine an arbitrary graph state's properties, including the possibility of teleportation and the relevant analytical criteria. By investigating the properties of several fundamental graph-state types, we identify a general strategy for optimizing excess noise due to finite squeezing. As an application, a general scheme for teleportation between two arbitrary parties on a two-dimensional square lattice cluster state is given, along with a cheaper yet equivalent optimization for fixed source-target teleportation. Finally, a universal way to distill bipartite entanglement from a graph-state entanglement network is presented based on the equivalence between teleportation and entanglement distillation.
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