  Quantum resources outperform classical ones for certain communication and
computational tasks. Remarkably, in some cases, the quantum advantage cannot be
improved using hypothetical postquantum resources. A class of tasks with this
property can be singled out using graph theory. Here we report the experimental
observation of an impossible-to-beat quantum advantage on a four-dimensional
quantum system defined by the polarization and orbital angular momentum of a
single photon. The results show pristine evidence of the quantum advantage and
are compatible with the maximum advantage allowed using postquantum resources.
