  The coupling of a quantum system to an environment leads generally to
decoherence, and it is detrimental to quantum correlations within the system
itself. Yet some forms of quantum correlations can be robust to the presence of
an environment - or may even be stabilized by it. Predicting (let alone
understanding) them remains arduous, given that the steady state of an open
quantum system can be very different from an equilibrium thermodynamic state;
and its reconstruction requires generically the numerical solution of the
Lindblad equation, which is extremely costly for numerics. Here we focus on the
highly relevant situation of ensembles of light emitters undergoing spontaneous
decay; and we show that, whenever their Hamiltonian is perturbed away from a
U(1) symmetric form, steady-state quantum correlations can be reconstructed via
pure-state perturbation theory. Our main result is that in systems of light
emitters subject to single-emitter or two-emitter driving, the steady state
perturbed away from the U(1) limit generically exhibits spin squeezing; and it
has minimal uncertainty for the collective-spin components, revealing that
squeezing represents the optimal resource for entanglement-assisted metrology
using this state.
