  Recent progress on quantum state engineering has enabled the preparation of
quantum photonic systems comprising multiple interacting particles.
Interestingly, multiphoton quantum systems can host many complex forms of
interference and scattering processes that are essential to perform operations
that are intractable on classical systems. Unfortunately, the quantum coherence
properties of multiphoton systems degrade upon propagation leading to undesired
quantum-to-classical transitions. Furthermore, the manipulation of multiphoton
quantum systems requires of nonlinear interactions at the few-photon level.
Here, we introduce the quantum van Cittert-Zernike theorem to describe the
scattering and interference effects of propagating multiphoton systems. This
fundamental theorem demonstrates that the quantum statistical fluctuations,
which define the nature of diverse light sources, can be modified upon
propagation in the absence of light-matter interactions. The generality of our
formalism unveils the conditions under which the evolution of multiphoton
systems can lead to surprising classical-to-quantum transitions. Specifically,
we show that the implementation of conditional measurements may enable the
all-optical preparation of multiphoton systems with attenuated quantum
statistics below the shot-noise limit. Remarkably, this effect had not been
discussed before and cannot be explained through the classical theory of
optical coherence. As such, our work opens new paradigms within the established
field of quantum coherence.
