Controlled Quantum Network Coding Without Loss of Information

Quantum network coding is used to solve the congestion problem in quantum communication, which will promote the transmission efficiency of quantum information and the total throughput of quantum network. We propose a novel controlled quantum network coding without information loss. The effective transmission of quantum states on the butterfly network requires the consent form a third-party controller Charlie. Firstly, two pairs of three-particle non-maximum entangled states are pre-shared between senders and controller. By adding auxiliary particles and local operations, the senders can predict whether a certain quantum state can be successfully transmitted within the butterfly network based on the Z- {vertical bar 0 >, vertical bar 1 >} basis. Secondly, when transmission fails upon prediction, the quantum state will not be lost, and it will still be held by the sender. Subsequently, the controller Charlie re-prepares another three-particle non-maximum entangled state to start a new round. When the predicted transmission is successful, the quantum state can be transmitted successfully within the butterfly network. If the receiver wants to receive the effective quantum state, the quantum measurements from Charlie are needed. Thirdly, when the transmission fails, Charlie does not need to integrate the X- {vertical bar+>, vertical bar->} basis to measure its own particles, by which quantum resources are saved. Charlie not only controls the effective transmission of quantum states, but also the usage of classical and quantum channels. Finally, the implementation of the quantum circuits, as well as a flow chart and safety analysis of our scheme, is proposed.