Multi-party quantum private comparison protocol base on $$$$-imensional entangle states

In this paper, a novel quantum private comparison protocol with \(l\)-party and \(d\)-dimensional entangled states is proposed. In the protocol, \(l\) participants can sort their secret inputs in size, with the help of a semi-honest third party. However, if every participant wants to know the relation of size among the \(l\) secret inputs, these two-participant protocols have to be executed repeatedly \(\frac{l(l-1)}{2}\) times. Consequently, the proposed protocol needs to be executed one time. Without performing unitary operation on particles, it only need to prepare the initial entanglement states and only need to measure single particles. It is shown that the participants will not leak their private information by security analysis.