This paper presents a systematic study of adversarial hypothesis testing for both quantum-quantum (QQ) and classical-quantum (CQ) channels. Unlike conventional channel discrimination, we consider a framework where the sender, Alice, selects the channel input adversarially to minimize Bob's distinguishability. We analyze this problem across four settings based on whether Alice employs i.i.d. or general inputs and whether the receiver, Bob, is informed of the specific input choice (allowing his measurement to depend on the input). We characterize the Stein exponents for each setting and reveal a striking distinction in behavior: for QQ channels with i.i.d. inputs, Bob's knowledge of the input significantly enhances distinguishability, yet this advantage vanishes when general inputs are permitted. In contrast, for CQ channels, Bob being informed provides a consistent advantage over the corresponding entanglement-breaking channels for both i.i.d. and general inputs. These results demonstrate a unique phenomenon in adversarial hypothesis testing where the CQ channel does not merely behave as a special case of the QQ channel.

翻译：本文系统研究了量子-量子（QQ）信道与经典-量子（CQ）信道的对抗性假设检验问题。与传统信道区分不同，我们考虑一种框架：发送方Alice以对抗方式选择信道输入，以最小化接收方Bob的可区分性。我们基于以下两个维度分析了该问题：Alice采用独立同分布输入或一般输入，以及接收方Bob是否知晓具体的输入选择（从而允许其测量依赖于输入）。我们刻画了每种设置下的Stein指数，并揭示了一个显著的行为差异：对于采用独立同分布输入的QQ信道，Bob知晓输入能显著增强可区分性，但当允许一般输入时，这一优势即消失。相反，对于CQ信道，无论采用独立同分布输入还是一般输入，Bob获知输入信息均能相对于对应的纠缠破坏信道带来持续优势。这些结果表明了对抗性假设检验中的一个独特现象：CQ信道并非仅表现为QQ信道的一种特例。