# Monogamy inequality for any local quantum resource and entanglement

## TL;DR

This paper establishes a general monogamy inequality linking local quantum resources and entanglement, revealing new bounds and relations that extend beyond traditional entanglement monogamy concepts.

## Contribution

It introduces a universal monogamy inequality applicable to any local quantum resource, based on convex measures and the relation between entanglement and local entropy.

## Key findings

- Derives a new monogamy inequality for local quantum resources and entanglement.
- Provides basis-independent bounds for local coherence.
- Shows the inequality applies to nonuniformity and coherence measures.

## Abstract

We derive a monogamy inequality for any local quantum resource and entanglement. It results from the fact that there is always a convex measure for a quantum resource, as shown here, and from the relation between entanglement and local entropy. One of its consequences is an entanglement monogamy different from that usually discussed. If the local resource is nonuniformity or coherence, it is satisfied by familiar resource and entanglement measures. The ensuing upper bound for the local coherence, determined by the entanglement, is independent of the basis used to define the coherence.