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We consider optimal state discrimination in a general convex operationalframework, so-called generalized probabilistic theories (GPTs), and present ageneral method of optimal discrimination by applying the complementarityproblem from convex optimization. The method exploits the convex geometry ofstates but not other detailed conditions or relations of states and effects. Wealso show that properties in optimal quantum state discrimination are shared inGPTs in general: i) no measurement sometimes gives optimal discrimination, andii) optimal measurement is not unique.

Structure of Optimal State Discrimination in Generalized Probabilistic Theories