The large number of τ leptons available at the Belle II experiment makes it possible to study their properties and the extent of their compositeness. We propose a strategy that relies on three observables defined in terms of elements of the polarization density matrix of the produced τ pairs, which we obtain via quantum tomography. We find that these observables can explore values of the magnetic dipole moment down to 6.3×10−4, which is 2 orders of magnitude better than the current experimental limit, constrain the electromagnetic radius below 4.3×10−3 fm, and exclude an electric dipole moment larger than 1.7×10−17 e cm. The quoted limits are at the 95% confidence level (CL) and are obtained for a benchmark integrated luminosity of 1 ab−1 and a Monte Carlo estimate of the statistical sensitivity. Published by the American Physical Society 2024