# A mathematical theory of resources

arXiv: https://arxiv.org/abs/1409.5531 · HTML: https://mlsanity.com/paper/1409.5531/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2014.

## Built on by (most cited first, 3 of 3)

- [On the statistical complexity of quantum circuits](https://mlsanity.com/paper/2101.06154/) (2021)
- [Effects of quantum resources on the statistical complexity of quantum circuits](https://mlsanity.com/paper/2102.03282/) (2021)
- [A Layered Architecture for Universal Causality](https://mlsanity.com/paper/2212.08981/) (2022)

## Abstract (arXiv)

In many different fields of science, it is useful to characterize physical states and processes as resources. Chemistry, thermodynamics, Shannon's theory of communication channels, and the theory of quantum entanglement are prominent examples. Questions addressed by a theory of resources include: Which resources can be converted into which other ones? What is the rate at which arbitrarily many copies of one resource can be converted into arbitrarily many copies of another? Can a catalyst help in making an impossible transformation possible? How does one quantify the resource? Here, we propose a general mathematical definition of what constitutes a resource theory. We prove some general theorems about how resource theories can be constructed from theories of processes wherein there is a special class of processes that are implementable at no cost and which define the means by which the costly states and processes can be interconverted one to another. We outline how various existing resource theories fit into our framework. Our abstract characterization of resource theories is a first step in a larger project of identifying universal features and principles of resource theories. In this vein, we identify a few general results concerning resource convertibility.