Characterization of optimal measurement effects

Characterize the constraints satisfied by measurement effects in optimal zero-type-I-error parallel protocols for subgroup-versus-Haar unitary testing.

Background

The paper derives structural locking conditions for the system marginal of an optimal protocol but emphasizes that these conditions do not characterize the full protocol. In particular, the converse does not determine the measurement effects associated with optimal probes.

The authors explicitly list constraints on optimal measurement effects as an open problem, leaving unresolved which additional representation-theoretic or resource-theoretic conditions optimal accepting and rejecting effects must satisfy.

References

Other open problems include uniform qutrit phase-space separation beyond nine queries, sufficient conditions for a locked marginal to be realizable by an optimal protocol, constraints on optimal measurement effects, and stability relative to the actual optimal-marginal~set.

— Resource Compatibility in Optimal Quantum Symmetry Testing  (2609.38134 - Cao et al., 29 Sep 2026) in Discussion