  We uncover a form of quantum contextuality that connects maximal
contextuality to boson indistinguihability in a similar way maximal nonlocality
with respect to the Clauser-Horne-Shimony-Holt Bell inequality is connected to
maximal entanglement. Unlike previous forms of photonic contextuality, this
form cannot be simulated with classical light, as it relies on
indistinguishability and higher-order interference. Ideal measurements on the
bosonic system can be performed by means of dispersive coupling with an
ancillary qubit. This allows us delaying at will the ending of each measurement
and targeting high-dimensional contextual correlations, which are features
which cannot be achieved with existing platforms.
