  We describe spontaneous parametric down-conversion experiments in which
induced coherence across two coupled interferometers results in high-visibility
single-photon interference. Opening additional photon channels allows
"which-path" information and reduces the visibility of the singlephoton
interference, but results in nearly perfect visibility when photons are counted
in coincidence. A simplified theoretical model accounts for these complementary
observations and attributes them directly to the relations among the vacuum
fields at the different crystals.
