LOCC monotonicity of the observable-correlations-based entanglement measure E_oc

Ascertain whether the entanglement measure E_oc(ρ), defined via maximized observable correlations and a convex-roof construction, is nonincreasing under LOCC; determine its status as a valid entanglement measure.

Background

E_oc is constructed from maximized mutual information over local measurements and extended to mixed states via a convex roof.

The authors state that it is unknown whether E_oc is nonincreasing under LOCC, casting doubt on its validity as an entanglement measure.

References

Notice here that whether $E_{oc}$ is nonincreasing under LOCC is unknown, so it may be not a well-defined entanglement measure in fact.

— Measure of entanglement and the monogamy relation: a topical review  (2512.21992 - Guo et al., 26 Dec 2025) in Section 2.3 Entanglement measure based on observable correlations