Characterizing SU(1,1) nonclassicality via variance

We quantify the nonclassicality of quantum states associated with the Lie group SU(1,1) by regarding states as observables and considering their variances in the SU(1,1) Perelomov coherent states. Combining the resolution of identity induced by the SU(1,1) Perelomov coherent states, we propose a quantifier for nonclassicality of a state based on the average uncertainty (variance) of the state (regarded as an observable) in the SU(1,1) Perelomov coherent states. This quantifier is easy to calculate and possesses several operational interpretations. We reveal its basic properties and illustrate it by several prototypical examples.