Abstract
In this thesis, we consider the quantum unambiguous discrimination problem of a set of linearly independent pure states. We propose a procedure to construct a POVM measurement for unambiguous quantum state discrimination. Base on this procedure, we justify that the necessary and sufficient condition for constructing an unambiguous discrimination POVM is equivalent to the condition for infinite quantum cloning. We develop methods to calculate the optimal discrimination efficiency for minimizing the inconclusive probability and the optimal discrimination efficiency for the minimax criterion. Finally, we prove a necessary and sufficient condition to have a POVM measurement which achieves the minimum inconclusive probability criterion and the minimax criterion simultaneously and show that geometrically uniform (GU) states with equal a priori probabilities meet this condition.