  As a modern approach for the foundation of quantum theory, existing studies
of General Probabilistic Theories gave various models of states and
measurements that are quite different from quantum theory. In this paper, to
seek a more realistic situation, we investigate models approximately close to
quantum theory. We define larger measurement classes that are smoothly
connected with the class of POVMs via a parameter, and investigate the
performance of perfect discrimination. As a result, we give a sufficient
condition of perfect discrimination, which shows a significant improvement
beyond the class of POVMs.
