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

Understand

Quantum channel discrimination is a fundamental problem in quantum information science.

• In this study, we consider general quantum channel discrimination problems, and derive the lower bounds of the error probability.
• Our lower bounds are based on the triangle inequalities of the Bures angle and the trace distance.
• As a consequence of the lower bound based on the Bures angle, we prove the optimality of Grover's search if the number of marked elements is fixed to some integer $\ell$.