  We experimentally demonstrate a mode-selective quantum frequency converter
over a compound spatio-temporal Hilbert space. We show that our method can
achieve high-extinction for high-dimensional quantum state tomography by
selectively upconverting the signal modes with a modulated and delayed pump. By
preparing the pump in optimized modes through adaptive feedback control,
selective frequency conversion is demonstrated with up to 30 dB extinction. The
simultaneous operations over high-dimensional degrees of freedom in both
spatial and temporal domains can serve as a viable resource for
photon-efficient quantum communications and computation.
