Quantum channel discrimination has been studied from an information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of unknown channel accesses. In this paper, we study the query complexity of quantum channel discrimination, wherein the goal is to determine the minimum number of channel uses needed to reach a desired error probability. To this end, we show that the query complexity of binary channel discrimination depends logarithmically on the inverse error probability and inversely on the negative logarithm of the (geometric and Holevo) channel fidelity. As a special case of these findings, we precisely characterize the query complexity of discriminating two classical channels and two classical-quantum channels. Furthermore, by obtaining an optimal characterization of the sample complexity of quantum hypothesis testing, including prior probabilities, we provide a more precise characterization of query complexity when the error probability does not exceed a fixed threshold. We also provide lower and upper bounds on the query complexity of binary asymmetric channel discrimination and multiple quantum channel discrimination. For the former, the query complexity depends on the geometric R\'enyi and Petz R\'enyi channel divergences, while for the latter, it depends on the negative logarithm of the (geometric and Uhlmann) channel fidelity. For multiple channel discrimination, the upper bound scales as the logarithm of the number of channels.

翻译：量子信道区分已从信息论角度得到研究，其中研究者关注错误概率随未知信道访问次数增加的最优衰减速率。本文研究量子信道区分的查询复杂度，其目标是确定达到期望错误概率所需的最小信道使用次数。为此，我们证明二元信道区分的查询复杂度与错误概率倒数的对数成正比，与（几何保真度与Holevo保真度）信道保真度负对数成反比。作为这些结论的特例，我们精确刻画了区分两个经典信道及两个经典-量子信道的查询复杂度。此外，通过获得包含先验概率的量子假设检验样本复杂度的最优刻画，我们为错误概率不超过固定阈值时的查询复杂度提供了更精确的描述。我们还给出了二元非对称信道区分与多元量子信道区分查询复杂度的上下界。对于前者，查询复杂度取决于几何Rényi散度与Petz Rényi信道散度；对于后者，则取决于（几何保真度与Uhlmann保真度）信道保真度的负对数。对于多元信道区分，其上界与信道数量的对数成正比。