Absence of Entanglement Growth in Dicke Superradiance

Dicke superradiance describes an ensemble of $N$ permutationally invariant two-level systems collectively emitting radiation with a peak radiated intensity scaling as $N^2$. Although individual Dicke states are typically entangled, the density matrix during superradiant decay is a mixture of such states, raising the subtle question of whether the total state is entangled or separable. We resolve this by showing analytically that for all $N$, starting from the fully excited state, the collective decay preserves separability for all times. This answers a longstanding question on the role of entanglement in Dicke superradiance and underscores that, despite collective dissipation, separable states remain separable under these dynamics.