Secure multiparty quantum computation for summation and data sorting

In this paper, we propose a protocol for quantum secure multiparty summation and privacy sorting based on inverse quantum Fourier transform. The protocol allows multiple participants to obtain the summation and sorting of their secrets without revealing their private inputs. Each participant in the protocol encodes his/her own secret input into the phase of the d-level entangled state of n particles by means of a phase transformation operator and an inverse quantum Fourier transform. Finally, all participants perform measurements and jointly calculate the sum of all the secret data, meanwhile deriving their own rankings of the private inputs based on the final results. Compared to the existing similar quantum summation and sorting protocols, this protocol requires only a one-time particle transmission and does not require private key sequences to encrypt secret information, resulting in higher quantum efficiency. The participants can further obtain the ranking of their secret inputs by themselves. The credibility of the protocol is demonstrated in security analysis and simulation.