  A sequential network of quantum operations is efficiently described by its
quantum comb, a non-negative operator with suitable normalization constraints.
Here we analyze the case of networks enjoying symmetry with respect to the
action of a given group of physical transformations, introducing the notion of
covariant combs and testers, and proving the basic structure theorems for these
objects. As an application, we discuss the optimal alignment of reference
frames (without pre-established common references) with multiple rounds of
quantum communication, showing that i) allowing an arbitrary amount of
classical communication does not improve the alignment, and ii) a single round
of quantum communication is sufficient.
