  We propose a general description on the unambiguous discrimination of mixed
states according to the system-environment coupling, and present a procedure to
reduce this to a standard semidefinite programming problem. In the two states
case, we introduce the canonical vectors and partly simplify the problem to the
case of discrimination between pairs of canonical vectors. By considering the
positivity of the two by two matrices, we obtain a series of new upper bounds
of the total success probability which depends on both the prior probabilities
and specific state structures.
