发表机构
Royal Holloway, University of London（伦敦大学皇家霍洛威学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将制备-测量场景的语境相关性线性代数框架扩展至任意级数顺序变换的操作场景，给出完整判定流程并分析复杂度，通过示例验证方法，揭示了组成结构在广义语境相关性中的重要作用。
AI 中文摘要
广义语境相关性是非经典广义概率理论（GPT，尤其是量子力学）的典型区分特性。对于给定广义概率理论的广义语境相关性的认证与表征方法，已在制备-测量及单级制备-变换-测量场景中得到充分发展。在近期工作[arXiv:2512.10000]中，提出了一种自底向上、优先统计的制备-测量场景语境相关性线性代数框架。我们将该方法扩展至含任意级数顺序变换的操作场景，给出了这类场景在操作理论中语境相关性的完整判定流程并分析其计算复杂度。具体而言，该判定流程的复杂度与最小GPT维度呈线性指数关系，与程序数量呈多项式关系。我们通过多个示例验证了该框架与方法，包括Spekkens玩具理论及8态单量子比特 stabilizer理论，还构造了一种仅在变换的顺序结构中显现语境相关性的操作理论。因此，我们的发现为组成结构在广义语境相关性现象中的重要作用提供了新的视角。
英文摘要
Generalized contextuality is a canonical distinguishing property of nonclassical generalized probabilistic theories, in particular quantum mechanics. Methods for certification and characterization of generalized contextuality of a given generalized probabilistic theory are well developed for prepare-measure and single-stage prepare-transform-measure scenarios. In a recent work [arXiv:2512.10000], a bottom-up, statistics-first linear-algebraic framework for contextuality in prepare-measure scenarios was introduced. We extend this approach to operational scenarios with sequential transformations with an arbitrary number of stages. We give a full decision procedure for contextuality of such scenarios within operational theories and analyze its computational complexity. In particular, our decision procedure has a complexity linearly exponential in the minimum generalized probabilistic theory (GPT) dimension, and polynomial in the number of procedures. We demonstrate our framework and approach through multiple examples, including Spekkens' toy theory and the 8-state single-qubit stabilizer theory. In particular, we construct an operational theory in which contextuality manifests itself only in the sequential structure of the transformations. Our findings thus shed new light on the significant role of compositional structures in the phenomenon of generalized contextuality.
Comments28 pages, one figure, comments are welcome
