# A note on robustness of coherence for multipartite quantum states

## TL;DR

This paper investigates the sub-additivity of the robustness of coherence (ROC) in multipartite quantum states, revealing that ROC can behave differently from other coherence measures and can be affected by state admixture.

## Contribution

It demonstrates that ROC can be sub-additive for certain multipartite states and explores how admixture influences this property, providing insights into coherence measure behaviors.

## Key findings

- ROC may be sub-additive for specific multipartite states
- Pairs of states can have different orderings under various coherence measures
- Numerical analysis shows differences in coherence measure orderings

## Abstract

In this brief report, we prove that robustness of coherence (ROC), in contrast to many popular quantitative measures of quantum coherence derived from the resource theoretic framework of coherence, may be sub-additive for a specific class of multipartite quantum states. We investigate how the sub-additivity is affected by admixture with other classes of states for which ROC is super-additive. We show that pairs of quantum states may have different orderings with respect to relative entropy of coherence, $l_{1}$-norm of coherence and ROC and numerically study the difference in ordering for coherence measures chosen pairwise.