标题： 量子假设排除的逆向界限：一种散度半径方法 显示英文标题

标题： Converse bounds for quantum hypothesis exclusion: A divergence-radius approach

摘要： 假设排除是一项信息论任务，其中实验者旨在从一组已知的候选假设中排除一个错误的假设，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的任务——其中假设分别由量子态和量子通道表示——在我们当前作者的最近工作中[Ji等，arXiv:2407.13728 (2024)]建立了关于渐近误差指数的有效可计算上界，其中推导基于非渐近分析。 在这篇我们之前工作的配套论文中，我们提供了相同的量子态和信道排除的渐近误差指数的上界的替代证明，但采用了与之前工作不同的概念性方法。 具体来说，我们将不对称二元假设检验的强逆结果应用于将任意“虚拟”假设与每个相关候选假设区分开来。 这通过一个几何启发式的论证得出了所需的以散度半径表示的上界。 显示英文摘要

摘要： 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.