  Starting with the quasi-Bell states of the qubit-oscillator system, we obtain
time evolution of the density matrix under the adiabatic approximation. The
composite density matrix leads to, via partial tracing of the qubit degree of
freedom, the reduced density matrix of the oscillator that is utilized to
obtain the quasi-probability distributions such as Glauber-Sudarshan P
function, Wigner W function and Husimi Q function. The negativity of the Wigner
function acts as a measure of the nonclassicality of the state. The negativity
becomes particularly relevant in understanding a comparison between the Wigner
entropy with the Wehrl entropy, which are based on the W function and Q
function, respectively.
