Monogamy exponent determination for general entanglement measures

Determine the monogamy exponent α(E) for bipartite entanglement measures beyond the currently known special multi-qubit cases, thereby identifying the minimal power for which E^α satisfies the monogamy inequality across higher-dimensional systems.

Background

The monogamy exponent α(E) characterizes the smallest power rendering the measure monogamous in the inequality form. It is known for some special measures and systems, but not generally.

The authors emphasize the exponent is still unknown outside certain multi-qubit scenarios.

References

Although we can prove the monogamy of almost all the entanglement monotones, the monogamy exponent is still unknown except for some special multi-qubit system with some special entanglement monotones.

— Measure of entanglement and the monogamy relation: a topical review  (2512.21992 - Guo et al., 26 Dec 2025) in Section 1 Introduction