Nonclassical States: An Observable Criterion

An observable criterion is derived that allows one to distinguish nonclassical states of the harmonic oscillator from those having a classical counterpart. A quantum state is shown to have no classical counterpart if and only if the characteristic functions of the quadrature distributions or the $s$-parametrized phase-space distributions exhibit a slower decay than for the ground state of the oscillator. This renders it possible to experimentally check the failure of the $P$ function to be a probability measure.