  We consider a state discrimination problem which deals with settings of
minimum-error and unambiguous discrimination systematically by introducing a
margin for the probability of an incorrect guess. We analyze discrimination of
three symmetric pure states of a qubit. The measurements are classified into
three types, and one of the three types is optimal depending on the value of
the error margin. The problem is formulated as one of semidefinite programming.
Starting with the dual problem derived from the primal one, we analytically
obtain the optimal success probability and the optimal measurement that attains
it in each domain of the error margin. Moreover, we analyze the case of three
symmetric mixed states of a qubit.
