Hierarchical controlled remote preparation of an arbitrary m-qudit state with four-qudit cluster states

We present a general scheme for hierarchical controlled remote preparation of an arbitrary m-qudit state by using m four-qudit cluster states as the quantum channel. The sender first performs m-qudit positive operator-valued measurement in accordance with her knowledge of prepared state and then performs generalized X -basis measurements on her entangled particles. The upper-grade agent only needs perform unitary operation in accordance with one of the lower-grade agents’ measurement results for controlled remote preparation of an arbitrary m-qudit state. The lower-grade agent needs perform corresponding unitary operations in accordance with all the other agents’ measurement results. The protocol has the advantage of transmitting less entangled particles for hierarchical controlled remote preparation of an arbitrary m-qudit state via four-qudit cluster states.