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