Generalized squeezing as a witness

Quantum systems can be prepared in an infinite continuum of states, but only some of them can be used as resources for quantum technologies. Discerning whether a specific quantum state falls into this class, is often a challenging task. We show that it can be performed by looking at the squeezing of the quantum states - a scenario in which the variance of some observable operator is suppressed below the threshold given by the non-useful states. We discuss the general concept first; then we illustrate the approach by evaluating cubic nonlinear squeezing in the system of collective atomic spins.