Any entanglement of assistance is polygamous

TL;DR

The paper introduces a new condition for quantum correlation measures to be considered polygamous, demonstrating that entanglement of assistance is polygamous while faithful entanglement measures are not.

Contribution

It presents an alternative polygamy condition for quantum correlations and clarifies the polygamous nature of entanglement of assistance versus faithful entanglement measures.

Findings

Entanglement of assistance is polygamous.

Faithful entanglement measures are not polygamous.

The new condition is equivalent to standard polygamy inequalities.

Abstract

We propose a condition for a measure of quantum correlation to be polygamous without the traditional polygamy inequality. It is shown to be equivalent to the standard polygamy inequalities for any continuous measure of quantum correlation with the polygamy power. We then show that any entanglement of assistance is polygamous but not monogamous and any faithful entanglement measure is not polygamous.