  Collective spontaneous emission occurs when multiple quantum emitters decay
into common radiation modes, resulting in enhanced or suppressed emission.
Here, we find the quantum state of light collectively emitted from emitters
exhibiting quantum correlations. We unveil under what conditions the quantum
correlations are not lost during the emission but are instead transferred to
the output light. Under these conditions, the inherent nonlinearity of the
emitters can be tailored to create desired photonic states in the form of
traveling single-mode pulses, such as Gottesman-Kitaev-Preskill and
Schr\"odinger-cat states. To facilitate such predictions, our work reveals the
multi-mode nature of collective spontaneous emission, capturing the role of the
emitters' positions, losses, interactions, and beyond-Markov dynamics on the
emitted quantum state of light. We present manifestations of these effects in
different physical systems, with examples in cavity-QED, waveguide-QED, and
atomic arrays. Our findings suggest new paths for creating and manipulating
multi-photon quantum light for bosonic codes in continuous-variable-based
quantum computation, communications, and sensing.
