An efficient two-party quantum private comparison protocol with decoy photons and two-photon entanglement

Following some ideas of the quantum secret sharing (QSS) protocol (2008, Phys. Lett. A 372, 1957), we propose an efficient quantum private comparison (QPC) protocol for comparing information of equality with the help of a third party (TP). The protocol can ensure fairness, efficiency and security. The protocol is fair, which means that one party knows the sound result of the comparison if and only if the other one knows the result. The protocol is efficient with the help of the TP for calculating. However, the TP cannot learn any information about the players' respective private inputs and even about the comparison result and cannot collude with any player. The protocol is secure for the two players, that is, any information about their respective secret inputs will not leak except the final computation result. A precise proof of security of the protocol is presented. Applications of this protocol may include private bidding and auctions, secret ballot elections, commercial business, identification in a number of scenarios and so on.