Complete Distributed Hyper-Entangled-Bell-State Analysis and Quantum Super Dense Coding

We propose a protocol to implement the distributed hyper-entangled-Bell-state analysis (HBSA) for photonic qubits with weak cross-Kerr nonlinearities, QND photon-number-resolving detection, and some linear optical elements. The distinct feature of our scheme is that the BSA for two different degrees of freedom can be implemented deterministically and nondestructively. Based on the present HBSA, we achieve quantum super dense coding with double information capacity, which makes our scheme more significant for long-distance quantum communication.