In this paper, we propose a novel quantum network coding scheme to achieve the perfect transmission of quantum states without loss of information. In our scheme, two pairs of non-maximally entangled states are pre-shared between senders. By applying the local operations at the sender, the perfect transmission of quantum states can be achieved on the butterfly network. Firstly, by adding auxiliary particles to the senders on the butterfly network, the senders can judge whether the quantum state transmission can be achieved or not in advance. The outstanding advantage of our scheme is that the transmission results of quantum states on the butterfly network can be predicted in advance. When the transmission fails, the quantum state will not be lost. The sender does not need to re-prepare the quantum state for retransmission. Secondly, in the proposed scheme, not only the resources of quantum channel and classical channel are greatly saved, but also only two-bit information is send through classical channel at the bottleneck. Thirdly, our scheme avoids preparing Bell basis to measure two-particle states and uses Z-basis and X-basis to measure single-particle states, which will make the experimental realization simplified. Finally, we also extend the scheme to the k-pair quantum network and give an example of quantum 3-pair network communication.

在本文中，我们提出了一种新颖的量子网络编码方案，可以在不丢失信息的情况下实现量子态的完美传输。在我们的方案中，发送者之间预先共享了两对非最大纠缠状态。通过在发送方应用本地操作，可以在蝶形网络上实现量子态的完美传输。首先，通过将辅助粒子添加到蝶形网络上的发送方，发送方可以提前判断是否可以实现量子态传输。该方案的突出优点是可以预先预测蝶形网络上量子态的传输结果。当传输失败时，量子态将不会丢失。发送者不需要为重新传输准备量子状态。其次，在该方案中，不仅大大节省了量子信道和经典信道的资源，而且在瓶颈处只能通过经典信道发送两位信息。第三，我们的方案避免了准备贝尔基础来测量两个粒子的状态并使用Z基和X基测量单粒子状态，这将简化实验实现。最后，我们还将方案扩展到k对量子网络，并给出了一个量子3对网络通信的示例。