Hierarchical Controlled Remote Preparation via the Brown State Under the Noisy Environment

Utilizing the Brown state as the quantum channel, we put forward a deterministic scheme to realize hierarchical controlled remote preparation of an arbitrary single-qubit state from the sender to anyone of the recievers. There exists a hierarchy among the receivers as far as the power to reconstruct the prepared state is concerned. The upper-grade receiver needs the cooperation of any two other receivers. While the receiver at the lower grade requires the support of all the remaining receivers. It means the receiver at the upper grade has greater power to recover initial state. Compared with the previous hierarchical controlled remote preparation protocols of an arbitrary single-qubit state, our scheme first uses Brown state as the entangled resource and has higher security as the upper-grade receiver needs the consents of at least two other receivers. In addition, we investigate the proposed scheme under the noisy environment.