Hierarchical controlled quantum communication via the χ state under noisy environment

Wang et al. first studied hierarchical quantum information splitting of an arbitrary single-qubit state via the [Formula: see text] 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 [Formula: see text] 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.