  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. Our secure network code can be applied to
several networks including the butterfly network.
