We investigate a state discrimination problem in operationally the most general framework to use a probability, including both classical, quantum theories, and more. In this wide framework, introducing closely related family of ensembles (which we call a Helstrom family of ensembles) with the problem, we provide a geometrical method to find an optimal measurement for state discrimination by means of Bayesian strategy. We illustrate our method in two-level quantum systems and in a probabilistic model with square-state space to reproduce, e.g., 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.
|ジャーナル||Physical Review A - Atomic, Molecular, and Optical Physics|
|出版ステータス||Published - 2009 6 9|
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