Efficient and Economic Schemes for Remotely Preparing a Four-Qubit Cluster-Type Entangled State

We propose two novel schemes for remotely preparing a four-qubit cluster-type entangled state (FCES) with complex coefficients by using four EPR pairs and two three-qubit GHZ states as the quantum channel, respectively. To complete the remote state preparation (RSP) schemes, several novel sets of four-and two-qubit measuring basis were introduced. In these schemes, after the sender performs two different projective measurements, the receiver should introduce two auxiliary qubits and employ suitable C-NOT gates on his qubits, the original state can be reconstructed with unit successful probability. Compared with the previous schemes for the RSP of a FCES, the advantage of the present schemes is that the entanglement resource can be reduced.