Classification and quantification of multipartite entanglement for arbitrary quantum states

Classify and quantify multipartite entanglement for arbitrary quantum states by developing general, scalable methods that distinguish entanglement types and provide robust measures across systems with more than two subsystems.

Background

Multipartite entanglement is substantially richer and more complex than bipartite entanglement. The authors explicitly cite its classification and quantification for arbitrary states as an unresolved problem, reflecting the lack of universally accepted frameworks to capture its many inequivalent forms.

Resolving this problem would provide foundational tools needed to compare and utilize entanglement in complex quantum systems, with implications for quantum computation, communication, and many-body physics.

References

In spite of continuous progress, the current state of entanglement theory is still marked by a number of outstanding unresolved problems. These problems range from the complete classification of mixed-state bipartite entanglement to entanglement in systems with continuous degrees of freedom, and the classification and quantification of multipartite entanglement for arbitrary quantum states.

— Epistemic vs Ontic Classification of quantum entangled states?  (1206.2916 - Caponigro et al., 2012) in Section 'Systems and Partitions', opening paragraph

Numerical analyses using two other measures of GTE, the three-$\pi$ entanglement and the genuine multipartite concurrence (GMC), likewise favor $k=1$. We have not established this selection rule analytically for these two measures and therefore do not include them among the main conclusions of this paper.

— Genuine Tripartite Entanglement Selects Gauge-Invariant Theories  (2608.18732 - Yamagishi, 19 Aug 2026) in Section 10, Conclusions

First, an analytic classification of rank-three and rank-four ranges that contain GHZ-SLOCC vectors but no GHZ-LU vector remains to be analyzed.

— Rank and Range Criteria for Mixed-State Determination from Local Marginals  (2608.24061 - Qiu et al., 25 Aug 2026) in Section 5, Conclusion and Further Perspectives

A complete $16\times16$ treatment tracking cross-DoF coherences, relevant when $\lambda$ is not small or the joint noise is non-isotropic, is left to future work.

— Photon-efficient quantum repeater chains via hyperentanglement-assisted purification  (2608.30786 - Kumar et al., 31 Aug 2026) in Appendix, Section Joint-isotropic generalization

The class-dependent behavior found in this work raises the question of whether the effect of controller assistance on the fidelity deviation is related to the underlying multipartite entanglement structure. In particular, it would be interesting to investigate whether the difference between the fidelity deviations with and without controller assistance can be quantitatively related to quantities characterizing three-qubit entanglement, such as the three-tangle, or to measures of genuine multipartite entanglement.

— Contrasting Effects of Control on Fidelity and Fidelity Deviation in Controlled Teleportation  (2609.01988 - Shin et al., 2 Sep 2026) in Conclusion, Section conclusion