Butterfly network coding based on bidirectional hybrid controlled quantum communication

Fusing the ideas of bidirectional hybrid controlled quantum communication and quantum network coding, we put forward a protocol for implementing butterfly network coding by using a five-qubit Brown state as the quantum channel. It shows that each source node could simultaneously teleport an arbitrary unknown single-qubit state to each destination node. Meanwhile, each destination node could remotely prepare an arbitrary known single-qubit state for their corresponding source node. Our protocol not only supports quantum teleportation but also supports remote state preparation. Furthermore, only Pauli operations, single-qubit measurements and Bell state measurements are used in our protocol, which provides great convenience for experimental realization. To the best of our knowledge, it is the first time that a protocol integrates bidirectional hybrid controlled quantum communication and quantum network coding. In this way, our protocol inherits the advantages of network coding, which can encode information on intermediate nodes and solve the bottleneck caused by communication path conflicts between nodes. Finally, we also compare the performance with other protocols. All in all, our protocol greatly expands the application range of quantum network coding, which has good potential to enhance the efficiency of communication in the quantum network.