Hierarchical remote preparation of an arbitrary multi-qubit state via Brown states

Considering the difference in the ability of agents to prepare target state and the highly entangled nature of the Brown state, we propose a hierarchical remote preparation scheme to prepare an arbitrary two-qubit state via Brown state. There are four agents who are classified into two grades with respect to their abilities of restoring the target state. The upper-grade agent can accomplish the task with the help of any two remaining agents. While the agent at the lower grade requires the cooperation of all the other agents. Compared with previous hierarchical remote preparation schemes for an arbitrary two-qubit state, our scheme offers enhanced security by necessitating the collaboration of at least two other agents for any single agent to prepare the target state. It is worth mentioning that the recovery operation of an agent, whether he is of upper or lower grade, can be derived from the general expression, which clearly reveals the relationship with the measurement results. Moreover, we extend the proposed scheme to the case of an arbitrary multi-qubit state, thereby enhancing the capacity for quantum information transfer. Additionally, we evaluated the impact of amplitude-damping noise and phase-damping noise on the proposed scheme.