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Recently, multiparty quantum key agreement (MQKA) protocols have gained increasing attention. Several MQKA protocols in the traveling mode have been proposed for higher key generation rates, which, however, are vulnerable to a collusive attack presented by Liu. In this paper, an analysis of Liu’s collusive attacks on Cao <italic>et al.</italic>’s protocol is given, based on which an efficient MQKA protocol that requires only sequential communication of a single <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>-level quantum system is put forward. Because of the single <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>-level quantum system, our protocol has huge advantages in scalability and can be realized with the state-of-the-art technology. The scalability means that each additional participant is only required to perform a unitary operator that is comparatively simple, and the complexity of measurements remains independent of the number of participants. Our protocol can also resist Liu’s collusive attacks due to the encrypted quantum channel and has an efficiency rate of <inline-formula> <tex-math notation="LaTeX">$\frac {1}{2N}$ </tex-math></inline-formula> (<inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> is the number of participants) that is much better than those of other quantum key agreement protocols. In addition, by using the proposed encoding method, a wide class of problems for which quantum information protocols based on multisystem entanglement can be mapped into much simpler ones involving only one system.

Efficient Multiparty Quantum Key Agreement With a Single $d$ -Level Quantum System Secure Against Collusive Attack