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 $\ell$. This result generalizes Zalka's result for $\ell=1$. We also present several numerical results in which our lower bounds based on the trace distance outperform recently obtained lower bounds.

翻译：量子信道歧视是量子信息科学中的一个基本问题。 在这项研究中, 我们考虑了普通量子频道歧视的问题, 并得出了差错概率的下限。 我们的下限是基于布尔斯角的三角不平等和痕量距离。 由于基于布雷斯角的下限, 如果标记元素的数量被固定在某种整数 $\ ell $ 上, 我们证明格罗弗的搜索是最佳的。 这个结果将Zalka的结果概括为$\ ell= $ $ $ = 1 。 我们还呈现了几个数字结果, 我们基于跟踪距离的下限最近获得的下限。