  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.
