In this paper, we proposed an unconditionally secure quantum Private Set Intersection Cardinality (PSI-CA) protocol. Compared with classical PSI-CA protocols, the proposed protocol can dramatically reduce the communication complexity, because it only requires O(1) communication cost, which is fully independent of the size of the sets. Furthermore, based on the proposed quantum PSI-CA protocol, we constructed a novel anonymous authentication scheme. This scheme can not only achieve two basic secure goals: secure authentication and anonymity, but can also dynamically update the authorized clients. When revoking any authorized client or adding a new client, it only needs to simply compute several set operations without any complex cryptographic operation, and thus it is very suitable for applications in some dynamic environments, e.g., large-scale client-server networks.