Not yet reviewed by Pith; the record is open.

We investigate the performance of quantum fisher information under the Unruh-Hawking effect, where one of the observers (eg, Rob) is uniformly accelerated with respect to other partners. In the context of relativistic quantum information theory, we demonstrate that quantum fisher information, as an important measure of the information content of quantum states, has a rich and subtle physical structure comparing with entanglement or Bell nonlocality. In this work, we mainly focus on the parameterized (and arbitrary) pure two-qubit states, where the weight parameter $\theta$ and phase parameter $\phi$ are naturally introduced. Intriguingly, we prove that $\mathcal{F}_\theta$ keeps unchanged for both scalar and Dirac fields. Meanwhile, we observe that $\mathcal{F}_\phi$ decreases with the increase of acceleration $r$ but remains finite in the limit of infinite acceleration. More importantly, our results show that the symmetry of $\mathcal{F}_\phi$ (with respect to $\theta=\pi/4$) has been broken by the influence of Unruh effect for both cases.