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Private comparison is a primitive for many cryptographic tasks, and recentlyseveral schemes for the quantum private comparison (QPC) have been proposed,where two users can compare the equality of their secrets with the help of asemi-honest third party (TP) without knowing each other's secret and withoutdisclosing the same to the TP. In the exisiting schemes, secrecy is obtained byusing conjugate coding, and considering all participants as quantum users whocan perform measurement(s) and/or create states in basis other thancomputational basis. In contrast, here we propose two new protocols for QPC,first of which does not use conjugate coding (uses orthogonal states only) andthe second one allows the users other than TP to be classical whose activitiesare restricted to either reflecting a quantum state or measuring it incomputational basis. Further, the performance of the protocols is evaluatedunder various noise models.

Orthogonal-state-based and semi-quantum protocols for quantum private comparison in noisy environment