  The generalized notion of noncontextuality provides an avenue to explore the
fundamental departure of quantum theory from a classical explanation. Recently,
extracting a different form of quantum advantage in various information
processing tasks has received an upsurge of interest. In a recent work [D.
Schmid and R. W. Spekkens, Phys. Rev. X 8, 011015 (2018)] it has been
demonstrated that discrimination of two nonorthogonal pure quantum states
entails contextual advantage when the states are supplied with equal prior
probabilities. We generalized the work to arbitrary prior probabilities as well
as to three arbitrary mirror-symmetric states. We show that the contextual
advantage can be obtained for any value of prior probability when only two
quantum states are present in the task. But surprisingly, in the case of three
mirror-symmetric states, the contextual advantage is available only for a
restrictive range of prior probabilities with which the states are prepared.
