Strong monotonicity of the robustness texture measure

Determine whether the robustness texture measure T_rob satisfies the strong monotonicity condition under texture-free operations.

Background

The paper compares several quantum-state texture measures against properties (T1)–(T5), including strong monotonicity (T4). For the robustness texture measure T_rob, the table does not establish whether strong monotonicity holds. The accompanying note explicitly records this as unresolved, so determining the property remains an open question within the proposed resource-theoretic framework.

References

It remains unclear whether $T_{rob}$ fulfills the strong monotonicity condition.

— Quantum-state texture measure and texture transformation  (2609.08163 - Lin et al., 8 Sep 2026) in Table 1, Note (ii) in the tablenotes of the table labeled "Property of texture measures"