Hierarchical remote preparation of an arbitrary two-qubit state with multiparty

Hierarchical remote preparation of an arbitrary two-qubit state has not been investigated by the previous work. We first put forward two deterministic schemes to realize the task among three agents by using two five-qubit cluster states as the quantum channel. To design these schemes, some useful and general measurement bases are constructed for the sender. Then, the two schemes are extended to multiparty with the aid of the symmetry of cluster state. There exists a hierarchy among the agents in terms of their ability to reconstruct the target state. The upper-grade agent requires the help of all the remaining upper-grade agents and anyone of the lower-grade agents. While the lower-grade agent needs the assistance of all the other agents. Finally, we consider the effect of two important decoherence noises: the amplitude-damping noise and phase-damping noise.