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。
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.