  The sequential unambiguous state discrimination (SSD) of two states prepared
in arbitrary prior probabilities is studied, and compared with three strategies
that allow classical communication. The deviation from equal probabilities
contributes to the success in all the tasks considered. When one considers at
least one of the parties succeeds, the protocol with probabilistic cloning is
superior to others, which is not observed in the special case with equal prior
probabilities. We also investigate the roles of quantum correlations in SSD,
and show that the procedure requires discords but rejects entanglement. The
left and right discords correspond to the part of information extracted by the
first observer and the part left to his successor respectively. Their relative
difference is extended by the imbalance of prior probabilities.
