# Flag Additivity in Quantum Resource Theories

## TL;DR

This paper introduces the concept of flag additivity in quantum resource theories, providing a unified property that helps derive key features like monotonicity and convexity, thereby advancing the theoretical understanding of quantum resources.

## Contribution

It proposes flag additivity based on tensor product structure as a new unified property for quantum resource theories, enabling derivation of other important properties.

## Key findings

- Flag additivity can be used to derive strong monotonicity.
- Flag additivity implies convexity of quantum resources.
- It leads to full additivity in quantum resource theories.

## Abstract

Quantum resource theories offer a powerful framework for studying various phenomena in quantum physics. Despite considerable effort has been devoted to developing a unified framework of resource theories, there are few common properties that hold for all quantum resources. In this paper, we fill this gap by introducing the flag additivity based on the tensor product structure and the flag basis for the general quantum resources. To illustrate the usefulness of flag additivity, we show that flag additivity can be used to derive other nontrivial properties in quantum resource theories, e.g., strong monotonicity, convexity, and full additivity.