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P2 A comonadic view of simulation and quantum resources

模拟与量子资源的余单子视角
LICS 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)2019匹配度 1/10 · 该论文研究量子资源理论、经验模型与余单子/co-Kleisli 范畴下的模拟,属于量子基础与范畴论形式语义;与用户关注的程序分析、Agentic/LLM、浮点程序分析、贝叶斯程序分析等方向均无直接交集。引用 18 inbox
Samson Abramsky, Rui Soares Barbosa, Martti Karvonen, Shane Mansfield
crossref: 2026-09-12

AI 速览

一句话:提出余单子与 co-Kleisli 范畴刻画经验模型间模拟,统一量子资源理论中的自由操作。

本文在层论式语境性与非局域性框架下研究模拟与量子资源。资源被行为化地表示为经验模型。作者推广并简化此前关于经验模型态射的工作:先引入非常简单的态射,再借助测量协议余单子,过渡到相应的 co-Kleisli 范畴,得到更有用的态射概念。结果表明,这些态射恰好刻画了语境性资源理论中通过“自由”操作获得的经验模型之间的模拟关系,并涵盖测量基量子计算方案中使用的经典控制类型。该工作用范畴论统一了量子资源与模拟,为资源理论提供结构视角。

问题
如何在层论语境性框架下为经验模型定义合适态射,以刻画量子资源之间的模拟关系。
方法
从简单的经验模型态射出发,利用测量协议余单子构造 co-Kleisli 范畴,从而得到更丰富的态射概念。
评估
通过范畴论论证证明该态射捕捉资源理论中“自由”操作导致的模拟,并覆盖测量基量子计算中的经典控制。
原文摘要(Abstract)

We study simulation and quantum resources in the setting of the sheaf-theoretic approach to contextuality and nonlocality. Resources are viewed behaviourally, as empirical models. In earlier work, a notion of morphism for these empirical models was proposed and studied. We generalize and simplify the earlier approach, by starting with a very simple notion of morphism, and then extending it to a more useful one by passing to a co-Kleisli category with respect to a comonad of measurement protocols. We show that these morphisms capture notions of simulation between empirical models obtained via “free” operations in a resource theory of contextuality, including the type of classical control used in measurement-based quantum computation schemes.

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BibTeX
@inproceedings{paperbot4977,
  title = {A comonadic view of simulation and quantum resources},
  author = {Samson Abramsky and Rui Soares Barbosa and Martti Karvonen and Shane Mansfield},
  booktitle = {LICS},
  year = {2019},
  doi = {10.1109/lics.2019.8785677}
}