  We continue the study of the quantum channel version of Shannon's zero-error
capacity problem. We generalize the celebrated Haemers bound to noncommutative
graphs (obtained from quantum channels). We prove basic properties of this
bound, such as additivity under the direct sum and submultiplicativity under
the tensor product. The Haemers bound upper bounds the Shannon capacity of
noncommutative graphs, and we show that it can outperform other known upper
bounds, including noncommutative analogues of the Lov\'asz theta function
(Duan-Severini-Winter, IEEE Trans. Inform. Theory, 2013 and
Boreland-Todorov-Winter, arXiv, 2019).
