Optimal partition count for general qutrit operator sets

Determine the optimal number of mutually commuting partitions required for the complete generalized Gell–Mann operator set in a general multi-qutrit system.

Background

The paper applies graph-coloring methods to partition operator sets into mutually commuting subsets, with each subset corresponding to one measurement setting. For complete multi-qubit Pauli sets, the optimal partition count is known, but the analogous optimum for general qutrit systems is not established. The authors therefore use integer-linear-programming results as reference optima only for problem sizes where the solver can complete.

References

In the general qutrit case, the optimal number of partitions is not known, so we treat the ILP results as reference optimal solutions whenever they can be obtained.

— Heuristically optimizing, synthesizing, and prioritizing measurement settings for quantum state tomography  (2609.02633 - Moudghalya et al., 2 Sep 2026) in Section 3.1, “Partitioning”