  Pairs of photons entangled in their time-frequency degree of freedom are of
great interest in quantum optics research and applications, due to their
relative ease of generation and their high capacity for encoding information.
Here we analyze, both theoretically and experimentally, the behavior of
phase-insensitive spectrally-resolved interferences arising from two pairs of
time-frequency entangled photons. At its core, this is a multimode entanglement
swapping experiment, whereby a spectrally resolved joint measurement on the
idler photons from both pairs results in projecting the signal photons onto a
Bell state whose form depends on the measurement outcome. Our analysis is a
thorough exploration of what can be achieved using time-frequency entanglement
and spectrally-resolved Bell-state measurements.
