Complete classification of mixed-state bipartite entanglement

Determine a complete classification of bipartite entanglement for mixed quantum states, establishing a comprehensive scheme that identifies and distinguishes all mixed-state entanglement types and separability classes in bipartite systems.

Background

The paper begins by noting that, despite progress, entanglement theory retains significant unresolved issues. Among these, the authors explicitly list the complete classification of mixed-state bipartite entanglement as an open challenge.

This problem concerns understanding and organizing all possible forms of entanglement in bipartite systems when states are mixed rather than pure, a central task in quantum information theory tied to separability criteria and entanglement measures.

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

For mixed states, no single spectrum determines a local-unitary orbit, and the right analogue of the spectral principle remains to be identified.

— Exact quantification of nonlocal magic  (2608.28563 - Sierant, 28 Aug 2026) in Discussion