Generalized squeezing as a witness of various quantum properties

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 nonuseful states. We discuss the general concept first; then, we illustrate the approach by evaluating cubic nonlinear squeezing in the system of collective atomic spins.