  We experimentally observe the quantum geometric tensor, namely the quantum
metric and the Berry curvature, for a square lattice of radiatively coupled
plasmonic nanoparticles. We observe a non-zero Berry curvature and show that it
arises solely from non-Hermitian effects. The quantum metric is found to
originate from a pseudospin-orbit coupling. The long-range nature of the
radiative interaction renders the behavior distinct from tight-binding systems:
Berry curvature and quantum metric are centered around high-symmetry lines of
the Brillouin zone instead of high-symmetry points. Our results inspire new
pathways in the design of topological systems by tailoring losses or gain.
