Computability of the quantum distance chromatic number

Determine whether the quantum k-distance chromatic number of a graph is a computable function.

Background

The paper introduces the quantum k-distance chromatic number χkq(G), defined equivalently as the quantum chromatic number of the kth power graph Gk. Although the paper establishes several spectral lower bounds for this parameter, it does not resolve its algorithmic computability. The authors explicitly identify computability as unknown, making this a foundational unresolved question about the parameter.