Suppression of decoherence with entanglement 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 the closed-form evolutions of fidelity, concurrence, global entanglement, and the relative entropy of coherence to describe the quantum dynamics in the CSM. For initial states with only intra-bath entanglement ( the Greenberger-Horne-Zeilinger-bath or the $W$-bath), their leading amplitudes of fidelity evolution both scale as $\mathcal O(1/N)$ with $N$ being the number of bath spins. However, when the central spin and the first bath spin constitute a maximal entangled pair in the initial state, the amplitude scaling of fidelity evolution declines from $\mathcal O(1/N)$ to $\mathcal O(1/N^2)$. That shows appropriate initial system-bath entanglement is contributive to suppress central spin decoherence. The role of such system-bath entanglement is further clarified by observing the trade-off relation between quantum coherence and entanglement dynamics. In addition, with the help of system-bath entanglement, we eventually realize quantum coherence-enhanced dynamics for the central spin where the consumption of bath entanglement is shown to play a central role.