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We address perfect discrimination of two separable states. When availablestates are restricted to separable states, we can theoretically consider alarger class of measurements than the class of measurements allowed in quantumtheory. The framework composed of the class of separable states and the aboveextended class of measurements is a typical example of general probabilistictheories. In this framework, we give a necessary and sufficient condition todiscriminate two separable pure states perfectly. In particular, we derivemeasurements explicitly to discriminate two separable pure states perfectly,and find that some non-orthogonal states are perfectly distinguishable.However, the above framework does not improve the capacity, namely, the maximumnumber of states that are simultaneously and perfectly distinguishable.

Perfect Discrimination of Non-Orthogonal Separable Pure States on Bipartite System in General Probabilistic Theory