Tight bound on finite-resolution quantum thermometry at low temperatures

Precise thermometry is of wide importance in science and technology in general and in quantum systemsin 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 optimalprecision scaling with temperature, as the temperature approaches zero. The bound demonstrates that underfinite resolution, the variance in any temperature estimate must decrease slower than linearly. This scalingcan be saturated by monitoring the nonequilibrium dynamics of a single-qubit probe. We support this findingby numerical simulations of a spin-boson model. In particular, this shows that thermometry with a vanishingabsolute error at low temperature is possible with finite resolution, answering an interesting question left openby previous work. Our results are relevant both fundamentally, as they illuminate the ultimate limits to quantumthermometry, and practically, in guiding the development of sensitive thermometric techniques applicable atultracold temperatures.