Optimal State Discrimination in Generic Probability Models

We investigate a state discrimination problem in generic probability models which include both classical and quantum theory. Closely related family of ensembles (which we call a Helstrom family of ensembles) with the problem is introduced and we provide a geometrical method to find an optimal measurement for state discrimination by means of Bayesian strategy. We illustrate our method in 2-level quantum systems, and reproduce the optimal success probabilities for binary state discrimination and N numbers of symmetric quantum states. The existences of families of ensembles in binary cases are shown both in classical and quantum theories in any generic cases.