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

Evolution of nonclassicality of the quasi-Bell states for a strongly coupled qubit-oscillator system