We study high-energy photons produced at a lepton collider that convert into an $e^{+}{e}^{-}$ pair in the detector, as a tool for measuring quantum information observables. We consider single- and double-conversion processes in $e^{+}{e}^{-}\to \gamma \gamma$ and $e^{+}{e}^{-}\to e^{+}{e}^{-}\gamma$. Single conversions enable an extraction of the spin-analyzing power, while double conversions probe polarization correlations. Focusing on the Belle-II detector, we show that, depending on the reconstruction resolution of the opening angle of the conversion $e^{+}{e}^{-}$ pair, quantum correlations of the diphoton system can be probed. In particular, measurements of violations of the Bell inequality, quantum discord, concurrence, nonstabilizerness, and steerability with spatially separated GeV-scale photons can be made at high significance.