  Encoding quantum information in the photon temporal mode (TM) offers a robust
platform for high-dimensional quantum protocols. The main practical challenge,
however, is to design a device that operates on single photons in specific TMs
and all coherent superpositions. The quantum pulse gate (QPG) is a
mode-selective sum-frequency generation designed for this task. Here, we
perform a full modal characterisation of a QPG using weak coherent states in
well-defined TMs. We reconstruct a full set of measurement operators, which
show an average fidelity of 0.85 to a theoretically ideal device when operating
on a 7-dimensional space. Then we use these characterised measurement operators
of the QPG to calibrate the device. Using the calibrated device and a
tomographically complete set of measurements, we show that the QPG can perform
high-dimensional TM state tomography with 0.99 fidelity.
