Nonclassicality of induced coherence witnessed by contextuality

Quantum indistinguishability by path identity generates a new way of optical coherence, called ``induced coherence". The phenomenon, originally uncovered by Zou, Wang, and Mandel's experiment, is an emerging notion in modern quantum experiments with a wide range of implications. However, there has been controversy over its true quantum nature and whether the result can be emulated with classical light. We design a suitable contextuality test that can determine the conditions under which the setting produces distinguishing quantum predictions that cannot be described classically, namely, via the noncontextual hidden variable model.