  We derive the optimal measurement for quantum state discrimination without a
priori probabilities, i.e. in a minimax strategy instead of the usually
considered Bayesian one. We consider both minimal-error and unambiguous
discrimination problems, and provide the relation between the optimal
measurements according to the two schemes. We show that there are instances in
which the minimum risk cannot be achieved by an orthogonal measurement, and
this is a common feature of the minimax estimation strategy.
