  Entangled photons (biphotons) in the time-frequency degree of freedom play a
crucial role in both foundational physics and advanced quantum technologies.
Fully characterizing them poses a key scientific challenge. Here, we propose a
theoretical approach to achieving the complete tomography of biphotons by
introducing a frequency shift in one arm of the combination interferometer. Our
method, a generalized combination interferometer, enables the reconstruction of
the full complex joint spectral amplitude associated with both frequency sum
and difference in a single interferometer. In contrast, the generalized
Hong-Ou-Mandel and N00N state interferometers only allow for the partial
tomography of biphotons, either in frequency difference or frequency sum. This
provides an alternative method for full characterization of an arbitrary
two-photon state with exchange symmetry and holds potential for applications in
high-dimensional quantum information processing.
