Can Hawking effect of multipartite state protect quantum resources in Schwarzschild black hole?

Most previous studies on relativistic quantum information have primarily focused on the vacuum state $|0\rangle$ and the first excited state $|1\rangle$ in two-mode entangled systems. In this work, we go beyond these limitations by considering arbitrary $q$-th excited states $|q\rangle$, aiming to investigate their role in preserving quantum resources. We analyze the influence of the Hawking effect on multipartite quantum states in the Schwarzschild spacetime, with particular attention to quantum entanglement and coherence. Our results show that, under the influence of the Hawking effect, increasing the excitation number $q$ leads to a reduction in quantum entanglement and mutual information, while enhancing quantum coherence. This indicates that the Hawking effect on excited multipartite states tends to degrade quantum correlations but simultaneously protects quantum coherence in curved spacetime. Therefore, when implementing quantum information protocols in gravitational settings, reducing the excitation number $q$ is favorable for maintaining entanglement, whereas increasing $q$ may be advantageous for tasks that rely on quantum coherence in relativistic quantum information processing.