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Hierarchical remote preparation of equatorial states has practical applications but has not been studied before. We first propose a deterministic protocol for two-dimensional equatorial states via a four-qubit cluster state. The sender can asymmetrically transmit the secret state to any one of the three agents who are ranked in terms of their authorities. A set of useful measurement bases is elaborately constructed which plays a key role in the protocol. Then the protocol is generalized to high-dimensional system. Further, taking advantage of cluster state's symmetry, we give a universal protocol with multiple agents. The high-grade agent needs the assistance of the remaining high-grade agents as well as one of the low-grade agents. While the low-grade agent needs the cooperation of all the other agents. The agents' recovery operators are expressed by a general formula which clearly reveals the relationship with the measurement results. Additionally, the impact of two kinds of noise is analyzed. [ABSTRACT FROM AUTHOR]

Wang et al. first studied hierarchical quantum information splitting of an arbitrary single-qubit state via the χ state as the entangled channel. There exists a hierarchy among the three receivers as far as the power to recover the teleported state is concerned. But the scheme is considered in ideal environment. In this paper, we reinvestigate the scheme in amplitude-damping and phase-damping noises. The fidelity and average fidelity are adopted to quantify the effect of noise. It is found that they are both dependent on the coefficients of the teleported state and the noise parameter. Moreover, we put forward a novel deterministic scheme to realize hierarchical controlled remote preparation of an arbitrary single-qubit state. Comparing with the previous scheme via the χ state, the sender does not need to perform information dividing due to the subtly constructed measurement basis. We also consider the proposed scheme under noisy environment. [ABSTRACT FROM AUTHOR]