Optimal covariant quantum networks

Abstract

A sequential network of quantum operations is efficiently described by its quantum comb [1], a non-negative operator with siutable 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 preestabUshed 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. © 2009 American Institute of Physics.