Abstract
In this article, an analytical description is presented based on the master equation. This master equation is formed from the system of superconducting phase qubit which is coupled to a torsional resonator and damped by a dispersive reservoir. An analytical approach for searching of some physical phenomena on the qubit system is presented, such as qubit inversion, purity and negativity. In addition, these phenomena are discussed for the resonance and off-resonance cases for many different initial states. From computational results, it is found that the mentioned phenomena depend on the dispersive reservoir parameter which leads to their death. However, the complete destruction of system coherence in the presence of dispersive reservoir leads to the death of entanglement between the qubit and torsional resonator.