  We propose in this note the study of quantum channels from association
schemes. This is done by interpreting the $(0,1)$-matrices of a scheme as the
Kraus operators of a channel. Working in the framework of one-shot zero-error
information theory, we give bounds and closed formulas for various independence
numbers of the relative non-commutative (confusability) graphs, or,
equivalently, graphical operator systems. We use pseudocyclic association
schemes as an example. In this case, we show that the unitary
entanglement-assisted independence number grows at least quadratically faster,
with respect to matrix size, than the independence number. The latter parameter
was introduced by Beigi and Shor as a generalization of the one-shot Shannon
capacity, in analogy with the corresponding graph-theoretic notion.
