Quantum systems can be used as probes in the context of metrology for enhanced parameter estimation. In particular, the delicacy of critical systems to perturbations can make them ideal sensors. Arguably the simplest realistic probe system is a spin- 12 impurity, which can be manipulated and measured in-situ when embedded in a fermionic environment. Although entanglement between a single impurity probe and its environment produces nontrivial many-body effects, criticality cannot be leveraged for sensing. Here we introduce instead the two-impurity Kondo model as a novel paradigm for critical quantum metrology, and examine the multiparameter estimation scenario at finite temperature. We explore the full metrological phase diagram numerically and obtain exact analytic results near criticality. Enhanced sensitivity to the inter-impurity coupling driving a second-order phase transition is evidenced by diverging quantum Fisher information (QFI) and quantum signal-to-noise ratio (QSNR). However, with uncertainty in both coupling strength and temperature, the multiparameter QFI matrix becomes singular—even though the parameters to be estimated are independent—resulting in vanishing QSNRs. We demonstrate that by applying a known control field, the singularity can be removed and measurement sensitivity restored. For general systems, we show that the degradation in the QSNR due to uncertainties in another parameter is controlled by the degree of correlation between the unknown parameters.

中文翻译：

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使用杂质探针的多参数临界量子计量


量子系统可以用作计量学背景下的探针，以增强参数估计。特别是，关键系统对扰动的敏感度可以使它们成为理想的传感器。可以说，最简单的现实探针系统是自旋 12 杂质，当嵌入费米子环境中时，可以对其进行原位操纵和测量。尽管单个杂质探针与其环境之间的纠缠会产生不平凡的多体效应，但无法利用临界性进行传感。在这里，我们引入了两种杂质近藤模型作为临界量子计量学的新范例，并检查了有限温度下的多参数估计场景。我们以数值方式探索完整的计量相图，并获得接近临界点的精确分析结果。发散的量子费希尔信息 (QFI) 和量子信噪比 (QSNR) 证明了对驱动二阶相变的杂质间耦合的敏感性增强。然而，由于耦合强度和温度的不确定性，多参数 QFI 矩阵变得奇异（即使要估计的参数是独立的），导致 QSNR 消失。我们证明，通过应用已知的控制场，可以消除奇点并恢复测量灵敏度。对于一般系统，我们表明，由于另一个参数的不确定性而导致的 QSNR 退化是由未知参数之间的相关程度控制的。