Quantum state exclusion is an operational task with application to ontological interpretations of quantum states. In such a task, one is given a system whose state is randomly selected from a finite set, and the goal is to identify a state from the set that is not the true state of the system. An error occurs if and only if the state identified is the true state. In this paper, we study the optimal error probability of quantum state exclusion and its error exponent from an information-theoretic perspective. Our main finding is a single-letter upper bound on the error exponent of state exclusion given by the multivariate log-Euclidean Chernoff divergence, and we prove that this improves upon the best previously known upper bound. We also extend our analysis to quantum channel exclusion, and we establish a single-letter and efficiently computable upper bound on its error exponent, admitting the use of adaptive strategies. We derive both upper bounds, for state and channel exclusion, based on one-shot analysis and formulate them as a type of multivariate divergence measure called a barycentric Chernoff divergence. Moreover, our result on channel exclusion has implications in two important special cases. First, when there are two hypotheses, our result provides the first known efficiently computable upper bound on the error exponent of symmetric binary channel discrimination. Second, when all channels are classical, we show that our upper bound is achievable by a parallel strategy, thus solving the exact error exponent of classical channel exclusion.

翻译：量子态排除是一种具有操作性的任务，应用于量子态的本体论解释。在此类任务中，给定一个系统，其状态从一个有限集合中随机选取，目标是识别出集合中一个非系统真实状态的状态。当且仅当所识别的状态即为真实状态时，发生错误。本文从信息论角度研究量子态排除的最优错误概率及其误差指数。我们的主要发现是基于多元对数欧几里得切尔诺夫散度给出的态排除误差指数的单字母上界，并证明该上界优于先前已知的最佳上界。我们还将分析扩展至量子信道排除，并为其误差指数建立了一个单字母且高效可计算的上界，该上界允许使用自适应策略。我们基于单次分析推导了态排除与信道排除的这两个上界，并将其表述为一类称为重心切尔诺夫散度的多元散度度量。此外，我们的信道排除结果在两个重要特例中具有意义。首先，当存在两个假设时，我们的结果为对称二元信道辨别的误差指数提供了首个已知的高效可计算上界。其次，当所有信道均为经典信道时，我们证明该上界可通过并行策略达到，从而解决了经典信道排除的精确误差指数问题。