Analytic tractability of restricted stabilizer problems with active dependencies

Determine which structured classes of active Pauli dependencies admit analytic resolution of the additional sign constraints that arise in restricted stabilizer problems.

Background

Restricted stabilizer problems can involve active dependencies among Pauli observables. According to the discussion, these dependencies generate additional sign constraints that are not captured solely by the frustration graph, potentially obstructing analytic treatment.

The paper exhibits centrally dressed operator families in the three- and four-site marginal analyses for which the dependencies can be resolved by decomposing the problem into a small number of central symmetry sectors. It leaves open the broader characterization of dependency structures that permit the same type of analytic resolution.

References

This connection raises a further question: when can a restricted stabilizer problem remain analytically tractable even in the presence of active Pauli dependencies?

— Such stuff as magic is made on: compact operator algebra, stabilizer polytope and the structure of reduced density matrices in a Kitaev spin liquid  (2609.03485 - Sabharwal et al., 3 Sep 2026) in Section 6.4, “Restricted observables and measurement resources”