论文标题
量子资源理论和可变域模态逻辑的功能性
Functoriality of Quantum Resource Theory and Variable-Domain Modal Logic
论文作者
论文摘要
量子资源理论是一种尖端工具，用于研究现实的操作约束下的量子机械原理的实际实现。它通过将量子系统建模为可能的或允许的实验操作的限制类别来实现这一目标。模态逻辑提供了一种用于研究可能性的正式工具，而不可能是一个完全一般的逻辑环境。在这里，我表明，量子资源理论可以用力地转化为可变域S4模态逻辑的模型，以提供新的形式技术来探索量子资源理论问题。然后，我通过将结构添加到这些逻辑模型中，以反映基础资源理论中资源的可转换性预订，将此功能关系扩展到一个注入性关系。我通过讨论如何具体部署这种观点来结束。
Quantum resource theory is a cutting-edge tool used to study practical implementations of quantum mechanical principles under realistic operational constraints. It does this by modelling quantum systems as restricted classes of possible or permissible experimental operations. Modal logic provides a formal tool for studying possibility and impossibility is a completely general logical setting. Here, I show that quantum resource theories may be functorially translated into models of variable-domain S4 modal logic in a way that provides a new class of formal techniques for exploring quantum resource-theoretic problems. I then extend this functorial relationship to an injective one by adding structure to these logical models to reflect the convertibility preorder of resources in the underlying resource theory. I conclude by discussing how this viewpoint may be deployed concretely.
