Precise thermometry is of wide importance in science and technology in general and in quantum systems in particular. Here, we investigate fundamental precision limits for thermometry on cold quantum systems, taking into account constraints due to finite measurement resolution. We derive a tight bound on the optimal precision scaling with temperature, as the temperature approaches zero. The bound demonstrates that under finite resolution, the variance in any temperature estimate must decrease slower than linearly. This scaling can be saturated by monitoring the nonequilibrium dynamics of a single-qubit probe. We support this finding by numerical simulations of a spin-boson model. In particular, this shows that thermometry with a vanishing absolute error at low temperature is possible with finite resolution, answering an interesting question left open by previous work. Our results are relevant both fundamentally, as they illuminate the ultimate limits to quantum thermometry, and practically, in guiding the development of sensitive thermometric techniques applicable at ultracold temperatures.

中文翻译：

---

低温下有限分辨率量子测温的紧密联系

精确的测温在整个科学技术中尤其是在量子系统中具有广泛的重要性。在这里，我们考虑到由于有限的测量分辨率而引起的限制，研究了冷量子系统上测温的基本精度极限。随着温度趋近于零，我们得出了最佳精度随温度变化的严格界限。该边界表明，在有限的分辨率下，任何温度估算值的方差必须比线性下降慢。通过监视单量子位探头的非平衡动态，可以使这种缩放饱和。我们通过自旋玻色子模型的数值模拟来支持这一发现。特别是，这表明在有限的分辨率下，低温下绝对误差消失的测温法是可行的，回答以前的工作遗留下来的一个有趣的问题。我们的结果从根本上相关，因为它们阐明了量子测温的极限，并且在实践中指导了适用于超冷温度的敏感测温技术的发展。