Broader applicability of the general property-testing technique

Determine the extent to which the witness-vector and acceptance-preserving path framework developed for fermionic Gaussianity and Slater determinant testing can be applied to other pure-state families and property-testing problems.

Background

The paper develops a general framework for testing membership in compact manifolds of pure quantum states. The approach combines a witness-vector bound for states with non-negligible overlap with the target family and a path argument that extends the bound to states with arbitrarily small overlap.

The framework is demonstrated for fermionic Gaussian states and Slater determinant states. The authors explicitly identify as unresolved the extent to which the technique can be applied more broadly to additional state families and testing settings.

References

Finally, although our second application, to Slater determinant testing, has not received as much prior interest in the community, we find the fact that our general technique goes through very smoothly to a second example to be encouraging; certainly the extent to which it can be more broadly applied is an interesting open question.

— Fermionic Gaussianity can be tested with mode-independent sample-complexity  (2610.02050 - West et al., 1 Oct 2026) in Section Discussion