Polygamy of entanglement of assistance for high-dimensional systems

Show whether the polygamy inequality holds for entanglement of assistance measures other than entanglement of formation of assistance and Tsallis-q entanglement of assistance in high-dimensional multipartite systems.

Background

The entanglement of assistance (E_a) is dual to convex-roof measures, and polygamy relations have been established for certain specific instances.

The authors explicitly state that, beyond E_{f,a} and E_{q,a}, polygamy remains open for other assisted measures in high dimensions.

References

Apart from $E_{f,a}$ and $E_{q,a}$, the polygamy relation for all other EoAs remain open for high dimensional systems.

— Measure of entanglement and the monogamy relation: a topical review  (2512.21992 - Guo et al., 26 Dec 2025) in Section 5.2 Entanglement of assistance is polygamous