Conjecture: Non–strict concavity of reduced functions for E_{V−k} for k≥2

Show that the reduced functions associated with Vidal’s $k$-indexed entanglement monotones $E_{V\text{-}k}$ are not strictly concave for all $k\geq 2$, extending the verified case $k=2$.

Background

The monogamy criterion relies on strict concavity of reduced functions.

The authors verify non–strict concavity for k=2k=2 and explicitly conjecture it for all k≥2k\geq 2.

References

It is not strictly concave when $k=2$. We conjecture that they are not strictly cave for all $k\geq 2$.

— Measure of entanglement and the monogamy relation: a topical review  (2512.21992 - Guo et al., 26 Dec 2025) in Section 3.8 Strict concavity of the reduced function (Table note d)