Many-body quantum resources of graph states

TL;DR

This paper introduces a scalable method to characterize many-body quantum correlations in various graph states, linking their quantum properties to potential quantum sensing applications, and classifies entanglement depth in small systems.

Contribution

It provides a simple, assumption-free technique to quantify many-body correlations in diverse graph states, including entanglement depth and usefulness for quantum sensing.

Findings

Characterized quantum correlations in four graph topologies.

Linked correlation strength to quantum sensing utility.

Classified entanglement depth in 8-qubit graph states into 146 classes.

Abstract

Characterizing the non-classical correlations of a complex many-body system is an important part of quantum technologies. A versatile tool for such a task is one that scales well with the size of the system and which can be both easily computed and measured. In this work we focus on graph states, that are promising platforms for quantum computation, simulation and metrology. We consider four topologies, namely the star graph states with edges, Tur\'an graphs, $r$-ary tree graphs, and square grid cluster states, and provide a method to characterise their quantum content: the many-body Bell correlations, non-separability and entanglement depth for an arbitrary number of qubits. We also relate the strength of these many-body correlations to the usefulness of graph states for quantum sensing. Finally, we characterize many-body entanglement depth in graph states with up to $8$ qubits in $146$ classes non-equivalent under local transformations and graph isomorphisms. The technique presented is simple and does not make any assumptions about the multi-qubit state, so it could find applications wherever precise knowledge of many-body quantum correlations is required.