Many-body quantum resources of graph states

Characterizing the non-classical correlations of a complex many-body system is an important part of quantum technologies. An ideal tool for this task would scale well with the size of the system, be easily computable and be easily measurable. In this work, we focus on graph states, which are promising platforms for quantum computation, simulation, and metrology. We consider four topologies: star graph states with edges, Turán graphs,<i>r</i>-ary tree graphs, and square grid cluster states. We provide a method to characterize their quantum content: many-body Bell correlations, non-separability and entanglement strength for an arbitrary number of qubits. We also relate the strength of these correlations to the usefulness of graph states for quantum sensing. Finally, we characterize many-body entanglement in graph states with up to eight qubits in 146 classes that are not equivalent under local transformations or graph isomorphisms. This technique is straightforward and does not require any assumptions about the multi-qubit state; therefore it could be applied wherever precise knowledge of many-body quantum correlations is necessary.