Invariants of the quantum graph of the partial trace

We compute the independence number, zero-error capacity, and the values of the Lovász function and the quantum Lovász function for the quantum graph associated to the partial trace quantum channel ${\mathrm{Tr}}_n\otimes {\mathrm{i}\mathrm{d}}_k\text{\hspace{0.17em}⁣}:\mathrm{B}({\mathbb{C}}^n\otimes {\mathbb{C}}^k)\to \mathrm{B}({\mathbb{C}}^k)$.