Transitive prime-dimensional ray-context arrangements

Construct a ray-context arrangement in prime dimension d=p that is ray-transitive and context-transitive, or even flag-transitive, under its symmetry group, and whose associated linear constraint system over F_p has a quantum-classical gap.

Background

The paper constructs ray-context arrangements yielding classically unsatisfiable linear constraint systems with finite-dimensional quantum solutions. The Harding–Jager–Smith construction provides highly symmetric examples in dimensions d=kn, but the authors then focus on the remaining prime-dimensional case d=p.

The authors explicitly note that their prime-dimensional construction does not have a single transitive orbit on rays and contexts. They ask whether a similarly highly symmetric construction can be found in prime dimension, while observing that such transitivity is not necessary for resolving the paper’s main existence problem. The question therefore remains an additional structural problem concerning the symmetry of quantum-classical-gap arrangements, rather than the existence of such gaps itself.