  We consider an interferometer based on the concept of induced coherence,
where two photons that originate in different second-order nonlinear crystals
can interfere. We derive a complementarity relationship that links the
first-order coherence between the two interfering photons with a parameter that
quantifies the distinguishing information regarding the nonlinear crystal where
they originated. We show that the derived relationship goes beyond the
single-photon regime and is valid for any photon-flux rate generated. We report
experimental results in the low photon-flux regime that confirm the validity of
the derived complementarity relationship.
