Efficient multi-party quantum key agreement protocol based on nonorthogonal quantum entangled pairs

Multi-party quantum key agreement protocols with traveling mode have attracted much attention due to their higher efficiency than protocols with distributing mode. Nevertheless, the structures with traveling mode are generally vulnerable to internal participants, i.e. collusive attack. In order to resist collusive attack, a multi-party quantum key agreement protocol based on nonorthogonal quantum pairs, bell states and their dualities, is proposed. In this paper, we propose the idea of mixed dense encoding on the Pauli operations and the Hadamard operation. The private key sequence of each participant is encoded into a sequence consisting of those single-particle unitary operations which will be performed on the nonorthogonal quantum pairs. In the end, all participants can extract the target common key by comparing the initial states with the final states of the nonorthogonal quantum pairs. The proposed structure has three considerable advantages. Firstly, thanks to the use of nonorthogonal quantum pairs and mixed encoding, the proposed protocol can resist collusive attack from internal participants efficiently. Secondly, the efficiency has been greatly improved. Furthermore, due to the fact that only quantum pairs and simple single-particle unitary transformations are used, the processions of the proposed protocols are simple and can be easily realized in current technology.