Tight Trade-off Between Internal, Assisted, and External Entanglement

TL;DR

This paper establishes a precise quantitative trade-off relation for entanglement distribution in three-qubit systems, linking internal, assisted, and external entanglement measures.

Contribution

It derives a tight, saturable monogamy relation that bounds the sum of concurrence and concurrence of assistance by external entanglement, unifying various entanglement constraints.

Findings

The monogamy relation is tight and saturable.

The bound decreases with increasing external entanglement.

Equivalent formulations in negativity are provided.

Abstract

We derive a tight and saturable monogamy relation for three-qubit pure states that bounds the sum of concurrence and concurrence of assistance by the entanglement with an external qubit. The bound decreases strictly with increasing external entanglement, establishing a precise trade-off between internal and environment-induced entanglement. Equivalent formulations in terms of negativity and its convex-roof extensions follow. Our result provides a unified and quantitative constraint on entanglement distribution in open multipartite quantum systems.