The dynamic characteristics of measured uncertainty and quantum coherence are explored for an inertial Unruh–DeWitt detector model in an expanding de Sitter space. Using the entropic uncertainty relation, the uncertainty of interest is correlated with the evolving time t, the energy level spacing δ, and the Hubble parameter H. The investigation shows that, for short time, a strong energy level spacing and small Hubble parameter can result in a relatively small uncertainty. The evolution of quantum coherence versus the evolving time and Hubble parameter, which varies almost inversely to that of the uncertainty, is then discussed, and the relationship between uncertainty and the coherence is explicitly derived. With respect to the l₁ norm of coherence, it is found that the environment for the quantum system considered possesses a strong non‐Markovian property. The dynamic behavior of coherence non‐monotonously decreases with the growth of evolving time. The dynamic features of uncertainty and coherence in the expanding space with those in flat space are also compared. Furthermore, quantum weak measurement is utilized to effectively reduce the magnitude of uncertainty, which offers realistic and important support for quantum precision measurements during the undertaking of quantum tasks.

中文翻译：

---

惯性Unruh-DeWitt检测器中的测量不确定度及其与量子相干性的关系

在扩展的de Sitter空间中，针对惯性Unruh-DeWitt检测器模型探索了测量不确定度和量子相干性的动态特性。使用熵不确定性关系，感兴趣的不确定性与演化时间t，能级间距δ和哈勃参数H相关。研究表明，在短时间内，强大的能级间距和较小的哈勃参数可能导致相对较小的不确定性。然后讨论了量子相干的演化与演化时间和哈勃参数的关系，它几乎与不确定性的变化成反比，并明确推导了不确定性和相干性之间的关系。关于l ₁根据相干规范，发现所考虑的量子系统的环境具有很强的非马尔可夫性质。相干的动态行为随着时间的增长而非单调地减少。还比较了扩展空间和平坦空间中不确定性和连贯性的动态特征。此外，利用量子弱测量有效地降低了不确定性的幅度，这为进行量子任务期间的量子精度测量提供了现实而重要的支持。