  The mismatch between elegant theoretical models and the detailed experimental
reality is particularly pronounced in quantum nonlinear interferometry (QNI).
In stark contrast to theory, experiments contain pump beams that start in
impure states and that are depleted, quantum noise that affects -- and drives
-- any otherwise gradual build up of the signal and idler fields, and nonlinear
materials that are far from ideal and have a complicated time-dependent
dispersive response. Notably, we would normally expect group velocity
mismatches to destroy any possibility of measurable or visible entanglement,
even though it remains intact -- the mismatches change the relative timings of
induced signal-idler entanglements, thus generating "which path" information.
Using a "positive-P" approach ideally suited to such problems, we show how the
time-domain entanglement crucial for QNI can be -- and is -- recoverable
despite the obscuring effects of real-world complications.
