Conventional optical synthesis, the manipulation of the phase and amplitude of spectral
components to produce an optical pulse in different temporal modes, is revolutionizing
ultrafast optical science and metrology. These technologies rely on the Fourier transform of
light fields between time and frequency domains in one-dimensional space. However, within
this treatment, it is impossible to incorporate the quantum correlation among photons. Here,
we expand the Fourier synthesis into high-dimensional space to deal with the quantum …