  We uncover emergent universality arising in the equilibration dynamics of
multimode continuous-variable systems. Specifically, we study the ensemble of
pure states supported on a small subsystem of a few modes, generated by
Gaussian measurements on the remaining modes of a globally pure bosonic
Gaussian state. We find that beginning from sufficiently complex global states,
such as random Gaussian states and product squeezed states coupled via a deep
array of linear optical elements, the induced ensemble attains a universal
form, independent of the choice of measurement basis: it is composed of
unsqueezed coherent states whose displacements are distributed normally and
isotropically, with variance depending on only the particle-number density of
the system. We further show that the emergence of such a universal form is
consistent with a generalized maximum entropy principle, which endows the
limiting ensemble, which we call the "Gaussian Scrooge distribution", with a
special quantum information-theoretic property of having minimal accessible
information. Our results represent a conceptual generalization of the recently
introduced notion of "deep thermalization" in discrete-variable quantum
many-body systems -- a novel form of equilibration going beyond thermalization
of local observables -- to the realm of continuous-variable quantum systems.
Moreover, it demonstrates how quantum information-theoretic perspectives can
unveil new physical phenomena and principles in quantum dynamics and
statistical mechanics.
