Optimal covariant quantum networks

TL;DR

This paper studies symmetric quantum networks called covariant combs, providing their structural properties and applying them to optimize reference frame alignment with minimal communication.

Contribution

It introduces covariant combs and testers, establishing their structure and applying these concepts to optimize quantum reference frame alignment protocols.

Findings

Classical communication does not improve alignment beyond quantum communication.

A single round of quantum communication suffices for optimal alignment.

Theoretical framework for covariant quantum networks and their symmetry properties.

Abstract

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.