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Abstract
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In line with an experimentally feasible protocol was proposed by A. Asadian et al. [
PRL 112, 190402 (2014)], we introduce a pure dephasing model where the interaction of
the central qubit with a nano-mechanical resonator is affected by a spin-bath to study the
dynamics of resonator-qubit entangled states. We show that how system-bath coupling as
well as the coupling among the bath’s spins, initial semi-classical states of the phonon as
well as the initial states of the bath, modify the entanglement of the system using measures
like concurrence. To gain insight into the effect of these correlations, we study the
dynamics of the mentioned setup both with and without initial correlations for arbitrary
system-environment coupling strengths. It is also shown that stable entanglement, which is
dependent on correlated initial states of the system-bath, their coupling strength, and bath
temperature, occurs even in the presence of decoherence.
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