Additivity of multipartite c-squashed entanglement

Determine whether the multipartite c-squashed entanglement E_sq^c(ρ) is additive, i.e., whether E_sq^c(ρ⊗σ)=E_sq^c(ρ)+E_sq^c(σ) holds in general.

Background

The authors define multipartite q- and c-squashed entanglement and report asymptotic continuity for both.

They explicitly state that the additivity of E_sqc remains open.

References

These two classes of multipartite entanglement monotones, $E_{sq}q$ and $E_{sq}c$ are shown to be asymptotically continuous. But whether $E_{sq}c$ is additive remains open.

— Measure of entanglement and the monogamy relation: a topical review  (2512.21992 - Guo et al., 26 Dec 2025) in Section 14.2 Squashed entanglement (multipartite)