  Maintaining coherence of a qubit is of vital importance for realizing a
large-scale quantum computer in practice. In this work, we study the central
spin decoherence problem in the $XXX$ central spin model (CSM) and focus on the
quantum states with different initial entanglement, namely intra-bath
entanglement or system-bath entanglement. We analytically obtain their
evolutions of fidelity, entanglement, and quantum coherence. When the initial
bath spins constitute an $N$-particle entangled state (the
Greenberger-Horne-Zeilinger-bath or the $W$-bath), the leading amplitudes of
their fidelity evolutions both scale as $\mathcal O(1/N)$, which is the same as
the case of a fully polarized bath. However, when the central spin is maximally
entangled with one of the bath spins, the amplitude scaling of its fidelity
evolution declines from $\mathcal O(1/N)$ to $\mathcal O(1/N^2)$. That implies
appropriate initial system-bath entanglement is contributive to suppress
central spin decoherence. In addition, with the help of system-bath
entanglement, we realize quantum coherence-enhanced dynamics for the central
spin where the consumption of bath entanglement is shown to play a central
role.
