Hypothesis exclusion is an information-theoretic task in which an experimenter aims at ruling out a false hypothesis from a finite set of known candidates, and an error occurs if and only if the hypothesis being ruled out is the ground truth. For the tasks of quantum state exclusion and quantum channel exclusion -- where hypotheses are represented by quantum states and quantum channels, respectively -- efficiently computable upper bounds on the asymptotic error exponents were established in a recent work of the current authors [Ji et al., arXiv:2407.13728 (2024)], where the derivation was based on nonasymptotic analysis. In this companion paper of our previous work, we provide alternative proofs for the same upper bounds on the asymptotic error exponents of quantum state and channel exclusion, but using a conceptually different approach from the one adopted in the previous work. Specifically, we apply strong converse results for asymmetric binary hypothesis testing to distinguishing an arbitrary ``dummy'' hypothesis from each of the concerned candidates. This leads to the desired upper bounds in terms of divergence radii via a geometrically inspired argument.

翻译：假设排除是一种信息论任务，其中实验者旨在从一组有限的已知候选假设中排除一个错误假设，且当且仅当被排除的假设是真实情况时才会发生错误。对于量子态排除和量子信道排除任务——其中假设分别由量子态和量子信道表示——在当前作者近期的工作中[Ji等人，arXiv:2407.13728 (2024)]，基于非渐近分析，建立了渐近错误指数的高效可计算上界。在我们先前工作的这篇配套论文中，我们为量子态和信道排除的相同渐近错误指数上界提供了替代证明，但采用了与先前工作概念上不同的方法。具体而言，我们将非对称二元假设检验的强逆结果应用于区分任意“虚拟”假设与每个相关候选假设。通过一个几何启发的论证，这导出了以散度半径表示的所需上界。