# A resource theory of superposition

## TL;DR

This paper develops a comprehensive resource theory for quantifying superposition in quantum states, extending coherence theories and establishing foundational properties and measures for superposition as a quantum resource.

## Contribution

It introduces a rigorous framework for superposition resource theory, generalizing coherence theories, and explores the structure of free operations and measures for superposition quantification.

## Key findings

- Connection between superposition and unambiguous state discrimination
- Development of several superposition measures
- Main results from coherence resource theories also apply to superposition

## Abstract

The superposition principle lies at the heart of many non-classical properties of quantum mechanics. Motivated by this, we introduce a rigorous resource theory framework for the quantification of superposition of a finite number of linear independent states. This theory is a generalization of resource theories of coherence. We determine the general structure of operations which do not create superposition, find an elementary connection to unambiguous state discrimination, and propose several general quantitative superposition measures. We show that several main results from resource theories of coherence still hold in our more general setting. Of special importance are two results about the free completion of trace decreasing operations and the free probabilistic transformation between pure states that are also valid for the special case of coherence.