Induced Coherence in Quantum and Classical Interferometry: Origin and Control

The wave-particle duality that manifests in the Young's double-slit interferometry satisfying the well known Englert-Greenberger-Yasin inequality has recently been shown to obey a universal triality relation involving coherence, predictability and rather surprisingly entanglement. In the present work, we explicitly demonstrate the persistence of the triality relation in the quantum induced coherence interferometer and the classical configuration recovers the well known duality inequality. Furthermore, we explore the origin of coherence and entanglement, in the induced coherence interferometer, and means to control them. We show that path indistinguishability (or intrinsic indistinguishability of the sources) in our setup plays a complementary role in influencing both interference and entanglement. We bring out manifestly the nature of coherence in both classical and quantum versions of induced coherence interferometers.