In this article, we propose a four-party double-direction quantum cyclic controlled remote state preparation scheme, where two-qubit states can be remotely prepared cyclically among three correspondents both in clockwise and counterclockwise directions simultaneously under the control of the supervisor. Before presenting our four-party scheme, we give the quantum circuit diagram for constructing the 25-qubit quantum entangled channel. In our scheme, each correspondent merely carries out a four-qubit projective measurement and the supervisor only need to perform a single-qubit measurement in the Z-basis. After obtaining the measurement results from the other two correspondents and the supervisor, each correspondent can restore the desired states perfectly by applying proper unitary operations. The proposed four-party scheme can also be extended to the case containing \(m(m>3)\) correspondents, by using a \((8m+1)\)-qubit entangled channel. Discussions show that the success probability of both the proposed four-party and \((m+1)\)-party schemes can reach 1. We also analyze the control power of the supervisor in our scheme. Detailed analysis demonstrates that the control power of the supervisor can also be guaranteed.

在本文中，我们提出了一种四方双向量子循环控制远程状态准备方案，其中可以在监督者的控制下同时在顺时针和逆时针方向的三个通信者之间循环地远程准备双量子位状态。在介绍我们的四方方案之前，我们给出了构建 25 量子比特量子纠缠通道的量子电路图。在我们的方案中，每个通信者仅进行四量子位投影测量，而监督者只需在 Z 基中进行单量子位测量。在从其他两个通讯员和主管那里获得测量结果后，每个通讯员都可以通过应用适当的单一操作完美地恢复所需的状态。\(m(m>3)\)通讯员，通过使用\((8m+1)\) -qubit 纠缠通道。讨论表明，所提出的四方和\((m+1)\)方方案的成功概率都可以达到1。我们还分析了我们方案中监督者的控制权。详细分析表明，监管者的控制权也可以得到保证。