Multi-party quantum private information comparison based on nonlocal orthogonal product states

In this work, the nonlocal quantum orthogonal product state (OPB) is first used to design a multi-party private comparison protocol, where multiple participants could securely compare the size of their private inputs. The ring topology is adopted for participants communicating with each other, which can significantly reduce the amount of information that the third party needs to process. But compared with the star topology, the ring topology is more vulnerable to the threat of participant attacks. Using the nonlocal OPB as the transmitted states can deal with this problem well, which prevents dishonest participants from obtaining valuable information related to the transmitted state. Vector coding, decoy particles, and random numbers are also used to promise the security of the protocol. In addition, this work requires less quantum capability. Compared with entangled states, nonlocal OPB is easier to prepare, and the operations that the participants need to perform are simple. The pre-shared key is not required, which consumes fewer quantum resources.