Wigner-positive optimality beyond nine qutrit-Clifford queries

Determine whether Wigner-positive optimality is possible for qutrit Clifford-versus-Haar testing with at least ten parallel queries.

Background

The paper establishes that Wigner-positive optimal protocols attain the unrestricted zero-type-I-error optimum at three and four queries, while no such protocol can attain the optimum from five through nine queries. The obstruction is proved using phase-space witnesses that separate Wigner-positive system marginals from the locked marginal set.

For query numbers beyond nine, the authors have not established either attainability or impossibility. The unresolved issue is therefore whether Wigner-positive probes and measurements can attain the unrestricted optimum for any or all query numbers m≥10.

References

For the qutrit Clifford group, Wigner-positive optimal protocols exist at three and four queries but not from five through nine; whether they exist beyond nine queries remains open.

— Resource Compatibility in Optimal Quantum Symmetry Testing  (2609.38134 - Cao et al., 29 Sep 2026) in Abstract; Introduction; Section “Qutrit Clifford group”