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We perform collective spin measurements to study the buildup of two-bodycorrelations between $\approx10^4$ spin $s=3$ chromium atoms pinned in a 3Doptical lattice. The spins interact via long range and anisotropic dipolarinteractions. From the fluctuations of total magnetization, measured at thestandard quantum limit, we estimate the dynamical growth of the connectedpairwise correlations associated with magnetization. The quantum nature of thecorrelations is assessed by comparisons with short and long time expansions,and numerical simulations. Our work shows that measuring fluctuations of spinpopulations provides new ways to characterize correlations in quantum many-bodysystems, for $s>1/2$ spins

Measuring correlations from the collective spin fluctuations of a large ensemble of lattice-trapped dipolar spin-3 atoms