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Abstract
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We introduce a unitary operator which may be constructed conveniently by exploiting
the properties of the Glauber displacement and parity operators. We show that it can
be considered as a constant of motion of a quantum system including pure dephasing
interaction of a central qubit with a nano-mechanical resonator. Using the eigenvectors
of the Glauber displacement operator, we paves a way for an extensive study of the
dynamics of resonator-qubit states. In addition, we show that the establishment of such
a constant of motion, which includes the parity operator, provides a way to introduce
a capable mechanical framework to generate some desired mechanical state as superposition of the Glauber coherent states. We investigate nonclassical properties of the
generated mechanical states, by evaluating mechanical-squeezing, Wigner function,
position–momentum entropic squeezing, and entanglement between spin-mechanical
modes. Furthermore, the pairwise classical and quantum correlations are derived based
on a necessary and sufficient condition for the zero-discord state. Finally, in order to
study the mechanical state’s behavior in an environment, we consider that the output
state is subject to amplitude (phase)-damping channels and their dissipative properties
are analyzed
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