Extend EBI-CBC ↔ n-IBC equivalence beyond the triple-wise case and beyond EBI

Establish, for general n ≥ 3 in qubit systems, whether the equivalence between Elegant Bell inequality contextuality-breaking channels (EBI-CBC) and n-incompatibility-breaking channels (n-IBC) holds, extending the direct connection shown in this work for the triple-wise case; and determine whether analogous equivalences hold for contextuality witnesses other than the Elegant Bell inequality (i.e., for other families of preparation-contextuality inequalities).

Background

The paper proves that for qubit channels there is a direct operational connection between contextuality-breaking channels witnessed via the noncontextual Elegant Bell inequality (EBI-CBC) and triple-wise incompatibility-breaking channels (3-IBC), and provides additional results for specific noise models. It also presents a partial generalization for depolarizing noise in scenarios with N measurements on one side, linking contextuality breaking to N-wise incompatibility breaking.

In the concluding section, the authors explicitly state that extending this connection to general n-wise incompatibility-breaking channels and exploring whether similar equivalences hold for other families of contextuality inequalities beyond EBI remains unresolved.