A novel multi-party semiquantum private comparison protocol of size relationship with d-dimensional single-particle states

By using d-level single-particle states, the first multi-party semiquantum private comparison (MSQPC) protocol which can judge the size relationship of private inputs from more than two classical users within one execution of protocol is put forward. This protocol requires the help of one quantum third party (TP) and one classical TP, both of whom are allowed to misbehave on their own but cannot conspire with anyone else. Neither quantum entanglement swapping nor unitary operations are necessary for implementing this protocol. TPs are only required to perform d-dimensional single-particle measurements. The correctness analysis validates the accuracy of the compared results. The security analysis verifies that both the outside attacks and the participant attacks can be resisted.