Perfect Quantum Network Coding Independent of Classical Network Solutions

Quantum network coding with classical assistance can transmit quantum information with fidelity one in error-free quantum channels. However, the dependency on classical network solutions leads to higher communication complexity and transmission congestion over a large-scale network with bottleneck channels. We find that certain types of quantum operation are sufficient to support multiple unicast sessions over the extended butterfly network. Furthermore, this construction decouples classical communication (assisting decoding information) from classical network solution. Based on this design, we propose an optimal protocol for this specific network, which significantly reduces the communication cost.