Optimal State Discrimination in General Probabilistic Theories

Abstract

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 {\it 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 2-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.

9 pages, 6 figures

References in corpus (3)

• Characterizing quantum theory in terms of information-theoretic constraints
• A generalized no-broadcasting theorem
• No-Signalling Bound on Quantum State Discrimination

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