# A Resource Theory of Quantum Measurements

## TL;DR

This paper develops a formal resource theory for quantum measurements, analyzing how measurements' ability to acquire information can be quantified and transformed, with implications for quantum state discrimination.

## Contribution

It introduces a novel resource theory framework for quantum measurements, focusing on information acquisition and establishing monotones and transformation constraints.

## Key findings

- Catalysis and purification are impossible in this resource theory.
- Standard information gain measures are resource monotones.
- Application to quantum state discrimination demonstrates practical relevance.

## Abstract

Resource theories are broad frameworks that capture how useful objects are in performing specific tasks. In this paper we devise a formal resource theory quantum measurements, focusing on the ability of a measurement to acquire information. The objects of the theory are equivalence classes of positive operator-valued measures (POVMs), and the free transformations are changes to a measurement device that can only deteriorate its ability to report information about a physical system. We show that catalysis and purification, protocols that are possible in other resource theories, are impossible in our resource theory for quantum measurements. Standard measures of information gain are shown to be resource monotones, and the resource theory is applied to the task of quantum state discrimination.