Generalized photon-bunching bounds in linear and non-linear quantum optical dynamics

To assess the capabilities of photonic quantum systems, it is essential to develop analytical and experimental methods for probing the underlying optical dynamics. Here, we investigate fundamental constraints arising when multi-photon states evolve through a quantum linear optical network, showing how such limitations can be overcome when introducing measurement-induced nonlinearities. Specifically, we analyze bounds related to photon-bunching behavior at the output of a linear interferometer and test them via a hybrid photonic platform realizing experiments with up to four photons. When the analysis is extended to a nonlinear regime, such bounds can be violated. We experimentally validate such behavior by employing an optical architecture featuring measurement-induced nonlinearity, thus introducing dynamics that go beyond standard linear optics. Our results highlight how the constraints implied by the linear optical formalism can be used as tools to test and characterize photonic models going beyond quantum linear optical dynamics.