Non-locality of conjugation symmetry: characterization and examples in quantum network sensing

TL;DR

This paper investigates the non-local resources needed for conjugation-symmetric measurements in quantum networks, introducing the magic-basis spectrum to characterize local measurability and exploring implications for quantum sensing.

Contribution

It introduces the magic-basis spectrum as a tool to characterize local measurability of conjugation symmetries in quantum networks and analyzes non-local resources for quantum sensing protocols.

Findings

The magic-basis spectrum characterizes local measurability of 2-qubit conjugations.

Conditions for locally implementable conjugation-symmetric measurements are derived.

Insights into non-local resources for quantum sensor networks are provided.

Abstract

Some quantum information processing protocols necessitate quantum operations that are invariant under complex conjugation. In this study, we analyze the non-local resources necessary for implementing conjugation-symmetric measurements on multipartite quantum networks. We derive conditions under which a given multipartite conjugation can have locally implementable symmetric measurements. In particular, a family of numbers called the ``magic-basis spectrum'' comprehensively characterizes the local measurability of a given 2-qubit conjugation, as well as any other properties that are invariant under local unitary transformations. We also explore the non-local resources required for optimal measurements on known quantum sensor networks by using their conjugation symmetries as a guide.