Full characterization of biphotons with a generalized quantum interferometer

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.