By exploiting an ancillary measured qubite and a system unitary evolution

a simpler method for state discrimination of qubits with a fixed inconclusive answer is given. The strategy includes the minimal error discrimination is zero as the probability of an inconclusive answer and the optimal unambiguous discrimination is some value as the probability of an inconclusive answer.The analytical solution was derived between the maximal total correct probability and the fixed inconclusive probability. By using an ancillary measured qubite

a unitary transformation acts on the whole initial system and the orthogonal measures on the output states can reach quantum state discrimination of two nonorthogonal states. The scheme itself provides an implementation of a positive operatorvalued measure of two nonorthogonal quantum states.