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Complete solutions are given in a closed analytic form for unambiguousdiscrimination of three general pure states with real mutual inner products.For this purpose, we first establish some general results on unambiguousdiscrimination of n linearly independent pure states. The uniqueness ofsolution is proved. The condition under which the problem is reduced to an(n-1)-state problem is clarified. After giving the solution for three purestates with real mutual inner products, we examine some difficulties inextending our method to the case of complex inner products. There is a class ofset of three pure states with complex inner products for which we obtain ananalytical solution.

Complete solution for unambiguous discrimination of three pure states with real inner products