High-capacity quantum private comparison protocol with two-photon hyperentangled Bell states in multiple-degree of freedom

In this paper, the first high-capacity quantum private comparison (QPC) protocol is proposed to solve the comparison problem of equality of two parties’ secret inputs without revealing them out. This scheme is assisted with the semi-honest third party to fulfill the task. And the genuine two-photon hyperentangled Bell states are utilized as the important information carriers. Different from the previous protocols, this hyperentangled Bell states are composed of only two photons but characterize six qubits in two longitudinal momentum and polarization degrees of freedom (DOFs). In addition, this protocol possesses a higher information capacity and saves massive quantum resources for that the two-photon system can carry 6 bits of information. Meanwhile, this scheme can be applied and useful for long-distance quantum communication to improve the feasibility of QPC protocol. Furthermore, 64 nonorthogonal single-photon states as decoy photons are utilized to detect the security of the quantum channel. This method not only increases the security of the quantum channel, but also decreases the decoherence effect of environment noise. Moreover, this QPC protocol is analyzed to be immune to various kinds of attack. Finally, this QPC protocol can obtain the good application to compare the secret inputs securely, efficiently and feasibly.