Temperature fluctuations of a finite system follow the Landau bound δT^{2}=T^{2}/C(T) where C(T) is the heat capacity of the system. In turn, the same bound sets a limit to the precision of temperature estimation when the system itself is used as a thermometer. In this paper, we employ graph theory and the concept of Fisher information to assess the role of topology on the thermometric performance of a given system. We find that low connectivity is a resource to build precise thermometers working at low temperatures, whereas highly connected systems are suitable for higher temperatures. Upon modeling the thermometer as a set of vertices for the quantum walk of an excitation, we compare the precision achievable by position measurement to the optimal one, which itself corresponds to energy measurement.
Temperature fluctuations of a finite system follow the Landau bound δT^{2}=T^{2}/C(T) where C(T) is the heat capacity of the system. In turn, the same bound sets a limit to the precision of temperature estimation when the system itself is used as a thermometer. In this paper, we employ graph theory and the concept of Fisher information to assess the role of topology on the thermometric performance of a given system. We find that low connectivity is a resource to build precise thermometers working at low temperatures, whereas highly connected systems are suitable for higher temperatures. Upon modeling the thermometer as a set of vertices for the quantum walk of an excitation, we compare the precision achievable by position measurement to the optimal one, which itself corresponds to energy measurement.
An optimal local quantum thermometer is a quantum many-body system that saturates the fundamental lower bound for the thermal state temperature estimation accuracy [L. Correa et al., Phys. Rev. Lett. 114, 220405 (2015)]. Such a thermometer has a particular energy-level structure with a single ground state and highly degenerated excited-state manifold, with an energy gap proportional to the estimated temperature. In this paper, we show that the optimal local quantum thermometer can be realized in an experimentally feasible system of spinless fermions confined in a one-dimensional optical lattice described by the Rice-Mele model. We characterize the system's sensitivity to temperature changes in terms of quantum Fisher information and the classical Fisher information obtained from experimentally available site occupation measurements.
The precision of a quantum thermometer is fundamentally constrained by the spectral structure of the probe itself, and a systematic mapping between the configurations of energy levels and thermometric performance provides relevant information to design optimized devices. In this work, we establish such a mapping by analyzing a broad class of quantum systems, ranging from finite spin ensembles and degenerate atoms to confining potentials, quantum walks, and continuous-spectrum models. We derive exact scaling laws for the quantum Fisher information, revealing two distinct high-temperature universality classes: finite-spectrum probes exhibit a T−4 decay, while unbounded or continuous spectra yield a slower T−2 decay. At low temperatures, we show that sensitivity, though universally exponentially suppressed, can be enhanced arbitrarily by engineering degenerate excited states or a quantum walk on a fully connected topology. By contrast, specific quantum walk topologies provide a distinct enhancement mechanism based on gap engineering, whereby an optimal network size yields an optimized T−2 low-temperature scaling. Furthermore, power-law spectra enable tunable scaling of thermometric performance with system size, offering a design principle for optimal probes in specific temperature windows. Our results contribute to transform spectral information into a resource for quantum thermometry, providing both fundamental bounds and practical guidelines to tailored temperature sensing.
Superconducting transmon systems are promising platforms for nanoscale thermometry due to their high sensitivity to environmental fluctuations. Their intrinsic anharmonicity, which is essential for qubit operations, gives rise to a non-equidistant energy spectrum that significantly affects the thermal populations and, consequently, the thermometric sensitivity. In this work, we investigate the ultimate quantum limits of temperature estimation with a transmon beyond the two-level approximation. We compare the thermometric performance of three complementary models: the qubit, a harmonic oscillator and a weakly anharmonic Duffing oscillator, evaluating their corresponding quantum Fisher information (QFI) as a function of the temperature. We show that the multilevel anharmonic structure of the transmon affects its thermometric precision. Indeed, including higher excited states enhances the maximum amount of information that can be extracted about the system temperature, compared to a qubit probe. Furthermore, we address a fundamental limitation of the standard quartic truncation, which yields a potential that is unbounded from below and supports only spurious metastable states. By introducing bounded anharmonic models, namely a confined quartic potential and a sextic correction term, we assess the robustness of the thermometric precision beyond the Duffing regime. Our results provide practical guidelines for transmon-based nanoscale thermometry and clarify the role of the anharmonic multilevel spectrum in quantum temperature estimation.
Abstract The heat capacity C of a given probe is a fundamental quantity that determines, among other properties, the maximum precision in temperature estimation. In turn, C is limited by a quadratic scaling with the number of constituents of the probe, which provides a fundamental limit in quantum thermometry. Achieving this fundamental bound with realistic probes, i.e. experimentally amenable, remains an open problem. In this work, we tackle the problem of engineering optimal thermometers by using networks of spins. Restricting ourselves to two-body interactions, we derive general properties of the optimal configurations and exploit machine-learning techniques to find the optimal couplings. This leads to simple architectures, which we show analytically to approximate the theoretical maximal value of C and maintain the optimal scaling for short- and long-range interactions. Our models can be encoded in currently available quantum annealers, and find application in other tasks requiring Hamiltonian engineering, ranging from quantum heat engines to adiabatic Grover’s search.
The precise measurement of low temperatures is significant for both the fundamental understanding of physical processes and technological applications. In this work, we present a method for low-temperature measurement that improves thermal range and sensitivity by generating quantum coherence in a thermometer probe. Typically, in temperature measurements, the probes thermalize with the sample being measured. However, we use a two-level quantum system, or qubit, as our probe and prevent direct probe access to the sample by introducing a set of ancilla qubits as an interface. We describe the open system dynamics of the probe using a global master equation and demonstrate that while the ancilla-probe system thermalizes with the sample, the probe per se evolves into a nonthermal steady state due to nonlocal dissipation channels. The populations and coherences of this steady state depend on the sample temperature, allowing for precise and wide-range low-temperature estimation. We characterize the thermometric performance of the method using quantum Fisher information and show that the quantum Fisher information can exhibit multiple and higher peaks at different low temperatures with increasing quantum coherence and the number of ancilla qubits. Our analysis reveals that the proposed approach, using a nonthermal qubit thermometer probe with temperature-dependent quantum coherence generated by a multiple qubit interface between a thermal sample and the probe qubit, can enhance the sensitivity of temperature estimation and broaden the measurable low-temperature range.
We discuss the application of techniques of quantum estimation theory and quantum metrology to thermometry. The ultimate limit to the precision at which the temperature of a system at thermal equilibrium can be determined is related to the heat capacity when global measurements are performed on the system. We prove that if technical or practical limitations restrict our capabilities to local probing, the highest achievable accuracy to temperature estimation reduces to a sort of mesoscopic version of the heat capacity. Adopting a more practical perspective, we also discuss the relevance of qubit systems as optimal quantum thermometers, in order to retrieve the temperature, or to discriminate between two temperatures, characterizing a thermal reservoir. We show that quantum coherence and entanglement in a probe system can facilitate faster, or more accurate measurements of temperature. While not surprising given this has been demonstrated in phase estimation, temperature is not a conventional quantum observable, therefore these results extend the theory of parameter estimation to measurement of non-Hamiltonian quantities. Finally we point out the advantages brought by a less standard estimation technique based on sequential measurements, when applied to quantum thermometry.