  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.
