Witnessing nonclassicality of a quantum oscillator state by coupling it to a qubit

We propose a witness operation for the nonclassical character of a harmonic oscillator state. The method does not require state reconstruction. For all harmonic oscillator states that are classical, a bound is established for the evolution of a qubit which is coupled to the oscillator. Any violation of the bound can be rigorously attributed to the nonclassical character of the initial oscillator state.