This paper proposes a three-dimensional (3D) controlled quantum teleportation scheme for an unknown single-qutrit state. The scheme is first introduced in an ideal environment, and its detailed implementation is described via the transformation of the quantum system. Four types of 3D-Pauli-like noise corresponding to Weyl operators are created by Kraus operators: trit-flip, t-phase-flip, trit-phase-flip, and t-depolarizing. Then, this scheme is analyzed in terms of four types of noisy channel with memory. For each type of noise, the average fidelity is calculated as a function of memory and noise parameters, which is afterwards compared with classical fidelity. The results demonstrate that for trit-flip and t-depolarizing noises, memory will increase the average fidelity regardless of the noise parameter. However, for t-phase-flip and trit-phase-flip noises, memory may become ineffective in increasing the average fidelity above a certain noise threshold.

本文提出了一种用于未知单量子态的三维（3D）受控量子隐形传态方案。该方案首先在理想环境中引入，通过量子系统的变换描述其具体实现。Kraus 算子创建了四种与 Weyl 算子相对应的类 3D-Pauli 噪声：trit-flip、t-phase-flip、trit-phase-flip 和 t-depolarizing。然后，针对四种带记忆的噪声信道对该方案进行了分析。对于每种类型的噪声，平均保真度计算为记忆和噪声参数的函数，然后与经典保真度进行比较。结果表明，对于 trit-flip 和 t-去极化噪声，无论噪声参数如何，记忆都会增加平均保真度。然而，