Quantum Thermometry in Open Quantum Systems

Quantum thermometry in open systems investigates how quantum probes exchange energy and information with their surrounding environment to measure temperature at microscopic scales. In such settings, the probe and sample typically interact continuously, necessitating a description beyond isolated systems. The theoretical framework combines open-system dynamics—often captured by master equations or the mean-force Gibbs state—with quantum estimation theory to identify optimal measurement strategies. Central quantities include the quantum Fisher information, which bounds achievable precision, and the heat capacity or thermal susceptibility of the probe, which dictates its sensitivity to temperature variations. Recent advances have clarified how finite probe–sample coupling, non-Gibbsian transient states and quantum coherences shape both the fundamental limits and practical realisations of nanoscale thermometers. Experimentally, implementations range from spin-network sensors and single-atom impurities in ultracold gases to engineered qubit and bosonic probes in solid-state devices. These developments open pathways to non-invasive, high-precision thermometry in condensed-matter research, quantum simulation platforms and emerging quantum technologies.

Research from Nature Portfolio

Recent foundational work established a generalised uncertainty relation for temperature estimation in the presence of non-negligible probe–sample interactions. By extending classical thermodynamic bounds with quantum estimation theory, this approach highlights additional fluctuations arising from the non-commutativity of the system state and its effective energy operator, revealing a dissipative correction to the signal-to-noise limit. Complementary research introduced the concept of local quantum thermal susceptibility, quantifying the ultimate accuracy of temperature estimation via strictly local measurements on a subsystem at equilibrium. This framework provides an operative measure of how ground-state distinguishability and excited-state structure influence low-temperature sensitivity, thereby offering a route to locate critical phenomena and optimise local thermometric schemes.

Research from all publishers

A perturbative theory of finite-coupling quantum thermometry has been developed to second order in the interaction strength. It demonstrates that local projective measurements of probe energy remain optimal for temperature estimation, with a closed-form expression for the quantum Fisher information guiding the design of practical sensors. In parallel, studies of low-temperature estimation have shown that generating and harnessing quantum coherences in a qubit probe—mediated by ancilla interfaces—can yield multiple sensitivity peaks and extend the measurable temperature range beyond what thermalisation alone permits. On the engineering front, networks of spin-½ particles have been configured to approach the fundamental quadratic scaling of heat capacity with system size, using machine-learning-optimised couplings. These architectures can be realised in current quantum annealing platforms, paving the way for scalable, high-precision thermometers and their integration into quantum heat engines and advanced sensing applications.

Quantum Thermometry in Open Quantum Systems publication trend

The graph below shows the total number of articles in quantum thermometry in open quantum systems across all publications each year (not limited to Nature Index journals).

Technical terms

Open quantum system: A quantum system that interacts continuously with an external environment, leading to dissipation and decoherence.

Mean-force Gibbs state: The reduced equilibrium state of a probe accounting for finite coupling to its thermal environment, generalising the Gibbs distribution.

Quantum Fisher information: A measure of the sensitivity of a quantum state to changes in a parameter—in this context, temperature—setting the lower bound on estimation variance.

Local quantum thermal susceptibility: The maximal precision achievable when estimating temperature using measurements confined to a subsystem of a larger equilibrium system.

References

1. Long-Time Equilibration Can Determine Transient Thermality. PRX Quantum (2023).
2. Energy measurements remain thermometrically optimal beyond weak coupling. Quantum (2023).
3. Optimal thermometers with spin networks. Quantum Science and Technology (2024).
4. Single-Atom Quantum Probes for Ultracold Gases Boosted by Nonequilibrium Spin Dynamics. Physical Review X (2020).
5. Energy-temperature uncertainty relation in quantum thermodynamics. Nature Communications (2018).
6. Local quantum thermal susceptibility. Nature Communications (2016).
7. Low-temperature quantum thermometry boosted by coherence generation. Physical Review Research (2023).