A Practical Quantum Network Coding Protocol Based on Non-Maximally Entangled State

In many earlier works, perfect quantum state transmission over the butterfly network can be achieved via quantum network coding protocols with the assist of maximally entangled states. However, in actual quantum networks, a maximally entangled state as auxiliary resource is hard to be obtained or easily turned into a non-maximally entangled state subject to all kinds of environmental noises. Therefore, we propose a more practical quantum network coding scheme with the assist of non-maximally entangled states. In this paper, a practical quantum network coding protocol over grail network is proposed, in which the non-maximally entangled resource is assisted and even the desired quantum state can be perfectly transmitted. The achievable rate region, security and practicability of the proposed protocol are discussed and analyzed. This practical quantum network coding protocol proposed over the grail network can be regarded as a useful attempt to help move the theory of quantum network coding towards practicability.