It is natural in a quantum network system that multiple users intend to send their quantum message to their respective receivers, which is called a multiple unicast quantum network. We propose a canonical method to derive a secure quantum network code over a multiple unicast quantum network from a secure classical network code. Our code correctly transmits quantum states when there is no attack. It also guarantees the secrecy of the transmitted quantum state even with the existence of an attack when the attack satisfies a certain natural condition. In our security proof, the eavesdropper is allowed to modify wiretapped information dependently on the previously wiretapped messages. Our protocol guarantees the secrecy by utilizing one-way classical information transmission (public communication) in the same direction as the quantum network although the verification of quantum information transmission requires two-way classical communication. In the protocol, some nodes may share secret randomness as resources in advance. Our secure network code can be applied to several networks including the butterfly network.

中文翻译：

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用于具有免费单向公共通信的通用多单播网络的单次安全量子网络编码


在量子网络系统中，多个用户很自然地将他们的量子消息发送到各自的接收者，这被称为多单播量子网络。我们提出了一种规范方法，可以从安全经典网络代码在多个单播量子网络上导出安全量子网络代码。当没有攻击时，我们的代码可以正确传输量子态。当攻击满足一定的自然条件时，即使存在攻击，它也保证了传输量子态的保密性。在我们的安全证明中，窃听者可以根据先前窃听的消息修改窃听的信息。尽管量子信息传输的验证需要双向经典通信，但我们的协议通过利用与量子网络相同方向的单向经典信息传输（公共通信）来保证保密性。在协议中，一些节点可以预先共享秘密随机性作为资源。我们的安全网络代码可以应用于包括蝴蝶网络在内的多种网络。