Internal entanglement and external correlations of any form limit each other

TL;DR

This paper establishes a fundamental relationship showing that the internal entanglement of a bipartite system and its external correlations with other systems mutually limit each other, with implications for quantum information measures.

Contribution

It introduces a general relation between internal entanglement and external correlations, demonstrating their mutual limitations across various correlation measures.

Findings

External correlations set an upper bound on internal entanglement.

Internal entanglement decreases as external correlations increase.

Quantum discord is also limited by external correlations.

Abstract

We show a relation between entanglement and correlations of any form. The internal entanglement of a bipartite system, and its correlations with another system, limit each other. A measure of correlations, of any nature, cannot increase under local operations. Examples are the entanglement monotones, the mutual information, that quantifies total correlations, and the Henderson-Vedral measure of classical correlations. External correlations, evaluated by such a measure, set a tight upper bound on the internal entanglement that decreases as they increase, and so does quantum discord.