Multi-party semi-quantum private comparison protocol of size relation based on d-dimensional single-particle states

Based on $d$-dimensional single-particle states, a new multi-party semi-quantum private comparison protocol is proposed. With the intervention of a semi-honest third party, multiple classical parties can determine the size relation to their respective privacies by executing the proposed protocol once. The remarkable feature of our protocol is that each classical participant only performs the unitary operation and the quantum rearrangement operation, which diminishes the utilization of quantum resources. The operations in the protocol are simulated on the IBM Quantum Computing Platform, and the simulation results manifest that the presented protocol is correct and workable. Moreover, this protocol attains a qubit efficiency of 16.67%. Finally, the security analysis testifies that our proposed protocol is robust against diverse outside and inside attacks.