Dicke states, spin squeezing and quantum metrology Dicke states are by definition simultaneous eigenstates of the $J_z$ and $J^2$ operator. What is the difference between these states and Dicke squeezed (DS) states? I know that these are "entangled" states which have many useful applications in quantum metrology.
 A: tl;dr: both have metrologically useful entanglement, but the way to extract such entanglement is different.
Dicke states have 0 variances of a particular measurement $\hat{J}_z$. Except for the two $|J_z=\pm J\rangle$ states, the Dicke states are metrologically usefully entangled since they have more than $2J$ Fisher information (see this review paper chap. II.C.4). On the other hand, Dicke states are non-Gaussian states. This indicates that one needs some statistical tools like Bayesian estimation to fully use the Fisher information, see same review paper chap. II.B.5-7.
The squeezed states, however, has Gaussian $S_\alpha$ distribution (except its average direction along $\langle\textbf{S}\rangle$). That makes it easier to use: in terms of signal-to-noise ratio (i.e., sensitivity), the squeezed state produces the same first-order signal while reducing the noise. This method saturates the Fisher information whenever the squeezing is not too strong to wrap around the Bloch sphere.
Also, Dicke states except the two stretched ones are hard to prepare; I don't think there are any results other than some very close to pole states like in this paper. Squeezed states, on the other hand, are much easier.
