Perfect quantum teleportation by four-particle cluster state

•The manuscript describes two quantum teleportation schemes with four-particle entangled cluster state.•An unknown single-particle pure state and an arbitrary two-particle pure entangled state are teleported.•The successful possibilities are both 100% about these two schemes.•Quantum channel fidelities are both 1 about these two schemes.

Two perfect quantum teleportation schemes for an unknown single-particle pure state and an arbitrary two-particle pure entangled state are proposed by using four-particle cluster state in this paper. As it is shown, the unknown single-particle pure state or the arbitrary two-particle pure entangled state can be teleported perfectly. The successful possibilities are both 100%100% and quantum channel fidelities are both 1 about these two schemes.