Functoriality of Quantum Resource Theory and Variable-Domain Modal Logic

TL;DR

This paper establishes a formal connection between quantum resource theories and variable-domain S4 modal logic, enabling new logical techniques to analyze quantum resources and their convertibility.

Contribution

It introduces a functorial translation of quantum resource theories into modal logic models and extends this to reflect resource convertibility, offering novel formal tools.

Findings

Quantum resource theories can be functorially mapped to S4 modal logic models.

The translation can be extended to reflect resource convertibility preorder.

This approach opens new avenues for analyzing quantum resources logically.

Abstract

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.