Quantum network coding for multi-unicast problem based on 2D and 3D cluster states

We mainly consider quantum multi-unicast problem over directed acyclic network, where each source wishes to transmit an independent message to its target via bottleneck channel. Taking the advantage of global entanglement state 2D and 3D cluster states, these problems can be solved efficiently. At first, a universal scheme for the generation of resource states among distant communication nodes is provided. The corresponding between cluster and bigraph leads to a constant temporal resource cost. Furthermore, a new approach based on stabilizer formalism to analyze the solvability of several underlying quantum multi-unicast networks is presented. It is found that the solvability closely depends on the choice of stabilizer generators for a given cluster state. And then, with the designed measurement basis and parallel measurement on intermediate nodes, we propose optimal protocols for these multi-unicast sessions. Also, the analysis reveals that the resource consumption involving spatial resources, operational resources and temporal resources mostly reach the lower bounds.