Abstract In order to solve the information leakage caused by dishonest intermediate nodes in quantum network coding, we apply quantum homomorphic encryption to the butterfly network, and propose a secure protocol for crossing two qubits. Firstly, in the communication process between two senders and the first intermediate node, two senders encrypt their measured particles and send them to the first intermediate node for encoding. If two intermediate nodes are dishonest and know the encryption rules between two senders and two receivers, or there is an external eavesdropper, none of them can recover the transmitted qubits of two senders from the encrypted transmitted particles. In this way, our protocol can transmit two qubits safely and crossly in the butterfly network. Secondly, by analyzing the internal participant attack and the external eavesdropper attack launched by dishonest intermediate nodes and an external eavesdropper respectively, it is confirmed that our protocol is secure. Finally, the experimental simulation results based on the Qiskit framework prove that our protocol is feasible.

中文翻译：

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基于量子同态加密的安全跨两个量子比特协议

摘要 为了解决量子网络编码中中间节点不诚实导致的信息泄露问题，我们将量子同态加密应用于蝶形网络，提出了一种跨两个量子比特的安全协议。首先，在两个发送者与第一个中间节点的通信过程中，两个发送者对自己的测量粒子进行加密，并发送给第一个中间节点进行编码。如果两个中间节点不诚实并且知道两个发送者和两个接收者之间的加密规则，或者存在外部窃听者，则它们都无法从加密的传输粒子中恢复两个发送者的传输量子比特。这样，我们的协议就可以在蝴蝶网络中安全交叉地传输两个量子比特。第二，通过分析不诚实的中间节点和外部窃听者分别发起的内部参与者攻击和外部窃听者攻击，证实了我们的协议是安全的。最后，基于 Qiskit 框架的实验仿真结果证明了我们的协议是可行的。