This Letter presents the first measurement of the impact-parameter dependent angular anisotropy in the decay of coherently photoproduced ρ0 mesons. The ρ0 mesons are reconstructed through their decay into pion pairs. The measured anisotropy corresponds to the amplitude of the cos⁡(2ϕ) modulation, where ϕ is the angle between the two vectors formed by the sum and the difference of the transverse momenta of the pions, respectively. The measurement was performed by the ALICE Collaboration at the LHC using data from ultraperipheral Pb–Pb collisions at a center-of-mass energy of sNN=5.02 TeV per nucleon pair. Different impact-parameter regions are selected by classifying the events in nuclear-breakup classes. The amplitude of the cos⁡(2ϕ) modulation is found to increase by about one order of magnitude from large to small impact parameters. Theoretical calculations describe the measured cos⁡(2ϕ) anisotropy and its impact-parameter dependence as the result of a quantum interference effect at the femtometer scale, arising from the ambiguity regarding which of the nuclei is the photon source in the interaction.