Witnessing entanglement of quantum spin liquids via covariance noise magnetometry with two diamond spin qubits

Dissipation in quantum systems, often considered as detrimental to the development of quantum computing platforms, has recently revealed promising applications in quantum metrology. In this context, noise can be harnessed to probe the quantum properties of exotic materials. Notably, NV (Nitrogen-Vacancy) sensors have emerged as a prominent platform for measuring local properties of magnetic materials. However, conventional measurement techniques are limited in accessing non-local properties. In this study, we propose a two NV sensor setup capable of detecting real-time detection of spin-spin correlations, even at extended distances. This innovative approach allows us to probe the dynamic structure factor, a property typically accessible only through neutron scattering experiments. We have evaluated the accuracy of this procedure using the Cramer-Rao bound and demonstrated its application to the Kitaev model. Our results reveal that quantum Fisher Information can be derived using this tabletop setup, thereby enabling us to characterize the entangled nature of such materials.