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