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.
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