# Monogamy relations of all quantum correlation measures for multipartite quantum systems

## TL;DR

This paper demonstrates that all quantum correlation measures obey monogamy relations in multipartite states and introduces tighter inequalities and new relations for multi-qubit pure states, enhancing understanding of quantum correlations.

## Contribution

It proves universal monogamy relations for all quantum correlation measures and develops improved inequalities and new relations for multi-qubit pure states.

## Key findings

- All quantum correlation measures satisfy monogamy relations.
- Tighter monogamy inequalities are established using residual quantum correlations.
- New monogamous relations are derived for multi-qubit pure states based on concurrence.

## Abstract

The monogamy relations of quantum correlation restrict the sharability of quantum correlations in multipartite quantum states. We show that all measures of quantum correlations satisfy some kind of monogamy relations for arbitrary multipartite quantum states. Moreover, by introducing residual quantum correlations, we present tighter monogamy inequalities that are better than all the existing ones. In particular, for multi-qubit pure states, we also establish new monogamous relations based on the concurrence and concurrence of assistance under the partition of the first two qubits and the remaining ones.