Complete discrimination of pure quantum states

This paper presents a complete discrimination strategy of pure quantum states, by which the accessible information about the input pure states can be obtained completely. The complete discrimination is showed by taking the example of discriminating symmetric pure states. The measurement operators of complete discrimination can be represented by the multi-order correct operators, and the m-order relative average correct probability in the figure of merit is introduced. Since the rank of an inconclusive operator is one and an inconclusive operator provides the minimum relative average correct probability, no more information about the input state can be extracted. Our strategy involves two standard discrimination strategies, namely minimum-error discrimination and unambiguous discrimination, while overcoming their deficiencies. It is promising for complete discrimination and may find important applications in quantum information science.