Deterministic separation of arbitrary photon pair states in integrated quantum circuits

Entangled photon pairs generated within integrated devices must often be spatially separated for their subsequent manipulation in quantum circuits. Separation that is both deterministic and universal can in principle be achieved through anti-coalescent two-photon quantum interference. However, such interference-facilitated pair separation (IFPS) has not been extensively studied in the integrated setting, where the strong polarization and wavelength dependencies of integrated couplers -- as opposed to bulk-optics beamsplitters -- can have important implications for performance beyond the identical-photon regime. This paper provides a detailed review of IFPS and examines how these dependencies impact separation fidelity and interference visibility. Focus is given to IFPS mediated by an integrated directional coupler. The analysis applies equally to both on-chip and in-fiber implementations, and can be expanded to other coupler architectures such as multimode interferometers. When coupler dispersion is present, the separation performance can depend on photon bandwidth, spectral entanglement, and the linearity of the dispersion. Under appropriate conditions, reduction in the separation fidelity due to loss of non-classical interference can be perfectly compensated for by classical wavelength demultiplexing effects. This work informs the design as well as the performance assessment of circuits for achieving universal photon pair separation for states with tunable arbitrary properties.