For the strategy of expanding dense coding protocols, firstly, a high-dimensional Hadamard matrix and CNOT gate are designed, and the encryption and decryption processes are implemented. Secondly, extend the protocol to multiple parties and consider attempting to establish an objective function for success probability when the initial resource is not the maximum quantum entangled state. Finally, we reconstruct the encryption and decryption processes in non-maximally entangled GHZ states. The research shows that this group of protocols is theoretically feasible in the infinite dimensional space, and confirms the advantages of high-dimensional entanglement, such as high channel capacity and strong anti-eavesdropping ability, which provides a good theoretical basis for in-depth research of high-dimensional entanglement in the field of quantum information.

针对扩展密集编码协议的策略，首先设计了高维Hadamard矩阵和CNOT门，并实现了加密和解密过程。其次，将协议扩展到多方，并考虑在初始资源不是最大量子纠缠态时尝试建立成功概率的目标函数。最后，我们重构了非最大纠缠 GHZ 状态下的加密和解密过程。研究表明这组协议在无限维空间理论上是可行的，并证实了高维纠缠的优势，如信道容量高、抗窃听能力强等，