# Hallmarking quantum states: unified framework for coherence and correlations

## TL;DR

This paper introduces a unified framework to quantify quantum coherence and correlations in multipartite states, revealing how coherence contributes to distributed quantum correlations and defining a new measure called 'hookup' for this purpose.

## Contribution

It proposes a novel measure that captures both local and global coherence contributions to quantum correlations in multipartite states, unifying previously separate concepts.

## Key findings

- Global coherence drives distributed quantum correlations.
- Local coherence also enhances the quantumness of states.
- The 'hookup' quantifier effectively measures total quantum resources.

## Abstract

Quantum coherence and distributed correlations among subparties are often considered as separate, although operationally linked to each other, properties of a quantum state. Here, we propose a measure able to quantify the contributions derived by both the tensor structure of the multipartite Hilbert space and the presence of coherence inside each of the subparties. Our results hold for any number of partitions of the Hilbert space. Within this unified framework, global coherence of the state is identified as the ingredient responsible for the presence of distributed quantum correlations, while local coherence also contributes to the quantumness of the state. A new quantifier, the "hookup", is introduced within such a framework. We also provide a simple physical interpretation, in terms of coherence, of the difference between total correlations and the sum of classical and quantum correlations obtained using relative-entropy--based quantifiers.