Complete characterization of pure-state UDA by local marginals

Characterize completely, in the settings where it remains unresolved, which multipartite pure quantum states are uniquely determined among all states by their prescribed local marginals.

Background

The paper places mixed-state uniqueness within the broader quantum marginal problem and notes that pure states have a simpler structure than mixed states. Although several special cases and exception classes are known, a complete characterization of pure-state uniqueness by local marginals is not available in most settings. This unresolved background problem motivates the study of mixed-state UDA criteria developed in the paper.

References

Pure states have a simpler structure and have therefore been studied extensively since the UDA problem was first introduced, although a complete characterization remains open in most settings.

— Rank and Range Criteria for Mixed-State Determination from Local Marginals  (2608.24061 - Qiu et al., 25 Aug 2026) in Section 1, Introduction