The second dielectric virial coefficients of helium and argon are investigated using a fully quantum statistical approach and recent accurate ab initio results for the interatomic potentials and the interaction-induced polarizabilities. We thereby extend a preceding investigation based on a semiclassical approach to include quantum effects. For helium the results support the findings of a previous study by Moszynski [J. Chem. Phys. 247, 440 (1995)] that quantum effects are substantial for temperatures below 10 K, while they are practically negligible above 70 K. For argon special care is needed in the numerical integrations carried out in the quantum statistical calculation of the virial coefficients, due to the presence of quasibound states in the continuum and a slow convergence of the summation over the angular momentum. Here quantum effects are practically negligible in the range of temperatures experimentally investigated, i.e., between 243 and 408 K. As far as comparison with experimental data is concerned, large discrepancies are found for some of the low-temperature experimental measurements of helium. Agreement is also unsatisfactory for high temperatures for argon and experimental redetermination is suggested.