The goal of quantum channel discrimination and estimation is to determine the identity of an unknown channel from a discrete or continuous set, respectively. The query complexity of these tasks is equal to the minimum number of times one must call an unknown channel to identify it within a desired threshold on the error probability. In this paper, we establish lower bounds on the query complexities of channel discrimination and estimation, in both the parallel and adaptive access models. We do so by establishing new or applying known upper bounds on the squared Bures distance and symmetric logarithmic derivative Fisher information of channels. Phrasing our statements and proofs in terms of isometric extensions of quantum channels allows us to give conceptually simple proofs for both novel and known bounds. We also provide alternative proofs for several established results in an effort to present a consistent and unified framework for quantum channel discrimination and estimation, which we believe will be helpful in addressing future questions in the field.

翻译：量子信道判别与估计的目标分别是从一个离散或连续集合中确定未知信道的身份。这些任务的查询复杂度等于在误差概率满足期望阈值范围内识别未知信道所需的最小调用次数。本文建立了信道判别与估计在并行访问模型和自适应访问模型中的查询复杂度下界。我们通过建立或应用已知的信道平方Bures距离与对称对数导数Fisher信息上界来实现这一目标。采用量子信道等距扩展的表述和证明框架，使我们能够为新颖及已知的边界提供概念简洁的证明。我们还对若干已有结论提供了替代证明，旨在构建量子信道判别与估计的一致统一框架，相信这将有助于解决该领域未来的问题。