Conjecture: Strict entanglement monotones are monogamous

Prove or refute the conjecture that all strict entanglement monotones—i.e., entanglement monotones whose reduced functions are strictly concave—are monogamous under the improved definition.

Background

The authors introduce strict entanglement monotones and show monogamy for many convex-roof instances but note some cases remain unresolved.

They explicitly conjecture that all strict entanglement monotones are monogamous.

References

However, it still remains unknown that whether or not the non convex-roof extended strict entanglement monotones in literature are monogamous in addition to the squashed entanglement and the one-way distillable entanglement. We conjecture that all the strict entanglement monotones are monogamous.

— Measure of entanglement and the monogamy relation: a topical review  (2512.21992 - Guo et al., 26 Dec 2025) in Section 3.9 Strict entanglement monotone