Fundamental limits on low-temperature quantum thermometry with finite resolution

TL;DR

This paper establishes fundamental limits on the precision of low-temperature quantum thermometry considering measurement resolution constraints, revealing mechanisms for sub-exponential scaling and illustrating with models like fermionic chains and Ising systems.

Contribution

It introduces a general theoretical framework for low-temperature quantum thermometry that accounts for measurement resolution and identifies bounds and mechanisms for improved precision.

Findings

Derived a fundamental bound on temperature measurement uncertainty with finite resolution.

Identified a mechanism for sub-exponential scaling in thermometry precision.

Demonstrated quadratic divergence of uncertainty in a fermionic chain model.

Abstract

While the ability to measure low temperatures accurately in quantum systems is important in a wide range of experiments, the possibilities and the fundamental limits of quantum thermometry are not yet fully understood theoretically. Here we develop a general approach to low-temperature quantum thermometry, taking into account restrictions arising not only from the sample but also from the measurement process. We derive a fundamental bound on the minimal uncertainty for any temperature measurement that has a finite resolution. A similar bound can be obtained from the third law of thermodynamics. Moreover, we identify a mechanism enabling sub-exponential scaling, even in the regime of finite resolution. We illustrate this effect in the case of thermometry on a fermionic tight-binding chain with access to only two lattice sites, where we find a quadratic divergence of the uncertainty. We also give illustrative examples of ideal quantum gases and a square-lattice Ising model, highlighting the role of phase transitions.