AI 中文总结
研究存在不完美检测时连续监测的 Kitaev 链的计量性质，利用费米子关联矩阵表征稳态，评估量子费舍尔信息等，发现不完美检测改变临界结构及相关计量增强，探测器效率有特定表现。
AI 中文摘要
我们研究了存在不完美检测时连续监测的 Kitaev 链的计量性质。系统以无点击记录为条件，每个发射的费米子仅以概率\(0\leq q\leq 1\)被记录。由于条件动力学保持高斯性，稳态完全由费米子关联矩阵表征。这允许直接评估量子费舍尔信息和平均乌尔曼曲率。对于完美检测，监测稳态保留奇异临界结构，关于化学势的量子费舍尔信息变为超广延的。对于任何\(q<1\)，不完美检测引入有限平滑长度，使奇点变圆并恢复广延标度。探测器效率表现为兼容的混合态估计参数，这由平均乌尔曼曲率消失表明。这些结果表明，不完整轨迹信息通过不同于普通热模糊的机制破坏与监测临界性相关的计量增强。
英文摘要
We study the metrological properties of a continuously monitored Kitaev chain in the presence of imperfect detection. The system is conditioned on a no-click record, while each emitted fermion is registered only with probability $0\leq q\leq 1$. Because the conditional dynamics remains Gaussian, the steady state is fully characterized by the fermionic correlation matrix. This allows a direct evaluation of the quantum Fisher information and of the mean Uhlmann curvature. For perfect detection, the monitored steady state retains a singular critical structure and the quantum Fisher information with respect to the chemical potential becomes super-extensive. For any $q<1$, imperfect detection introduces a finite smoothing length that rounds the singularity and restores extensive scaling. The detector efficiency behaves instead as a compatible mixed-state estimation parameter, as signaled by the vanishing mean Uhlmann curvature. These results show that incomplete trajectory information destroys the metrological enhancement associated with monitored criticality through a mechanism that differs from ordinary thermal smearing.
Comments6 pages, 3 figures
