Optimal covariant quantum networks

Understand

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.