AI 中文总结
该研究在广义概率理论框架下，揭示了能提供上下文优势的态集合的可区分性受非平凡上界约束，存在权衡关系，还将相关界应用于广义奇偶 oblivious 复用任务。
AI 中文摘要
量子信息中的核心问题之一是，给定的一组态能否在某些信息处理任务中提供优势。我们建立了两类问题间的普适联系：一组态的可区分程度，以及其能否驱动优势源于广义上下文性的任务。在广义概率理论（GPTs）框架下（该框架包含量子和经典系统作为特例），我们证明：任何能在上下文性驱动的任务中提供非经典优势的态集合，必须满足所有使用该完整集合的态区分任务的成功概率的非平凡上界。因此，上下文优势意味着有限的可区分性，揭示了两类基本操作资源间的权衡。重要的是，这不止是关于理想极限的表述：完美可区分性并非排除上下文性的必要条件。我们的阈值严格小于1，因此任何区分性能超过阈值但仍非完美可区分的态集合，必然存在非上下文解释。这些界源于态集合的简单几何性质——线性相关性，具有闭合解析形式，且仅依赖于任务的先验和态的凸几何。作为示例，我们将其应用于广义奇偶 oblivious 复用，其中该任务的足够高成功概率意味着码本的至少一个子系综无法驱动任何上下文优势。
英文摘要
A central question in quantum information is whether a given set of states can provide an advantage in some information-processing task. We establish a universal connection between two such questions: how well a set of states can be discriminated, and whether it can power tasks whose advantage stems from generalized contextuality. Working in the framework of generalized probabilistic theories (GPTs), which includes quantum and classical systems as special cases, we show that any set of states able to provide a nonclassical advantage in a contextuality-powered task must obey nontrivial upper bounds on the success probability of every state discrimination task using the full set. Contextual advantage therefore implies limited distinguishability, exposing a trade-off between two basic operational resources. Importantly, this is more than a statement about the idealized limit: perfect distinguishability is not needed to preclude contextuality. Our thresholds lie strictly below unity, so any set whose discrimination performance exceeds them while still imperfectly distinguishable is already guaranteed to admit a noncontextual explanation. The bounds follow from a simple geometric property, linear dependence of the state set, take a closed analytical form, and depend only on the prior of the task and the convex geometry of the states. As an illustration, we apply them to generalized parity-oblivious multiplexing, where sufficiently high success in the task implies that at least one sub-ensemble of the codebook cannot power any contextual advantage.
CommentsComments welcome! 8.5+5 pages, 4 figs
