Decoherence dynamics of entangled quantum states in the $XXX$ central spin model

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.