Propagation of quantum distance-chromatic separations

Determine whether a separation in the quantum k-distance chromatic number implies a separation in the quantum ℓ-distance chromatic number for every ℓ ≤ k.

Background

The paper relates quantum distance-k colorings to ordinary quantum colorings of graph powers through the identity χkq(G) = χq(Gk). Existing work studies separations between classical and quantum chromatic numbers, and the authors explain that analogous results apply to quantum distance-chromatic parameters. They leave unresolved whether a separation at distance k necessarily persists, in the corresponding sense, at every smaller distance ℓ.