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Quantum channel discrimination is a fundamental problem in quantuminformation science. In this study, we consider general quantum channeldiscrimination problems, and derive the lower bounds of the error probability.Our lower bounds are based on the triangle inequalities of the Bures angle andthe trace distance. As a consequence of the lower bound based on the Buresangle, we prove the optimality of Grover's search if the number of markedelements is fixed to some integer $\ell$. This result generalizes Zalka'sresult for $\ell=1$. We also present several numerical results in which ourlower bounds based on the trace distance outperform recently obtained lowerbounds.

Lower bounds on the error probability of multiple quantum channel discrimination by the Bures angle and the trace distance