Quantum Network Coding on Networks with Arbitrarily Distributed Hidden Channels

Although perfect quantum network coding has been proved to be achievable, it is still puzzling whether it is feasible whenever one or more of the channels are replaced by the hidden ones emerging from quantum entanglement. The question is answered in this paper. First, we propose a quantum network coding protocol over a butterfly network with two hidden channels. Second, we investigate a more general situation, where d-level quantum letters are transmitted through the network containing arbitrarily distributed hidden channels, and prove that quantum network coding on such networks is still achievable.