Finite generic separating family for qubit–qutrit mixed states

Identify a finite family of polynomial local-unitary invariants that separates generic qubit–qutrit mixed-state orbits while also resolving nongeneric orbit strata.

Background

The ordinary marginal-word Bargmann invariants do not separate all qubit–qutrit local-unitary orbits, even when the complete infinite family of words is used. The paper notes that the generic qubit–qutrit orbit space has real dimension 24, but separating generic orbits is not sufficient by itself: a complete finite family must also distinguish nongeneric states with enhanced stabilizers or spectral degeneracies.

References

Several problems remain open. A finite separating family for generic qubit--qutrit mixed states is not identified here; the generic orbit space has real dimension $24$, but a complete separating set must also resolve nongeneric strata.

— Bargmann Invariants Are Insufficient for Complete Local-Unitary Orbit Discrimination  (2609.11090 - Zhang et al., 10 Sep 2026) in Section 7, Conclusions

Several problems remain open. A finite separating family for generic qubit--qutrit mixed states is not identified here; the generic orbit space has real dimension $24$, but a complete separating set must also resolve nongeneric strata. It would be useful to characterize the subsets of state space on which ordinary marginal-word invariants remain complete, for instance under nondegeneracy assumptions on the marginal spectra. A further problem is to determine which additional invariants admit efficient estimation through multivariate trace protocols or collective measurements.

— Bargmann Invariants Are Insufficient for Complete Local-Unitary Orbit Discrimination  (2609.11090 - Zhang et al., 10 Sep 2026) in Section 7, Conclusions