Quantum hypothesis testing for composite alternative hypotheses

Much of the research in quantum hypothesis testing has focused on simple hypotheses. In practical situations, though, we need to consider more complex, or composite, hypotheses. This paper introduces an approach for testing these composite hypotheses in quantum systems. It combines repeating projective measurements with the quantum Neyman-Pearson test including quantum correlations, which improves the effectiveness of the tests. We also clarify theoretically how the type-II error (false negative) probability of the proposed test behaves asymptotically and show that the proposed test is better at distinguishing hypotheses than traditional approaches. In addition, through numerical calculation, we demonstrate that the proposed test enhances performance in quantum statistical models, where we usually use the classical binomial test. This result shows the practical benefits of applying quantum correlations in hypothesis testing scenarios.