Accurate measurement at low temperatures is essential for both gaining a fundamental understanding of physical processes and developing technological applications. In this paper, we propose a theoretical framework for quantum temperature sensing in a composite environment with non-Markovian dynamics. Our suggested system uses a single qubit as a temperature sensor to test its sensitivity in calculating the temperature of a composite environment. We show that the temperature sensor's sensitivity can saturate the quantum Cramér-Rao bound by measuring the σ[over ̂]_{z} observable of the probe qubit. Temperature sensing performance is measured using the quantum signal-to-noise ratio. We underline how non-Markovianity can enhance the performance of our thermometers. Furthermore, we emphasize that nonequilibrium conditions do not always result in the best sensitivities in temperature estimation.
Accurate measurement at low temperatures is essential for both gaining a fundamental understanding of physical processes and developing technological applications. In this paper, we propose a theoretical framework for quantum temperature sensing in a composite environment with non-Markovian dynamics. Our suggested system uses a single qubit as a temperature sensor to test its sensitivity in calculating the temperature of a composite environment. We show that the temperature sensor's sensitivity can saturate the quantum Cramér-Rao bound by measuring the σ[over ̂]_{z} observable of the probe qubit. Temperature sensing performance is measured using the quantum signal-to-noise ratio. We underline how non-Markovianity can enhance the performance of our thermometers. Furthermore, we emphasize that nonequilibrium conditions do not always result in the best sensitivities in temperature estimation.
We investigate quantum thermometry using a single-qubit probe embedded in a non-Markovian environment, employing the numerically exact hierarchical equations of motion (HEOM) to overcome the limitations of Born-Markov approximations. Through a systematic analysis of the dynamical and steady-state behavior of the quantum signal-to-noise ratio (QSNR) for temperature estimation, we identify several key findings that challenge the conventional expectation that strong coupling necessarily enhances thermometric performance. In nonequilibrium dynamical thermometry, weak system-environment coupling generally yields the optimal QSNR, whereas in the steady-state regime, strong coupling enhances sensitivity only in the ultralow-temperature limit, while weak coupling significantly improves precision at moderately low temperatures. To optimize performance across coupling regimes, we develop a hybrid computational framework that integrates HEOM with quantum-enhanced particle swarm optimization, enabling precise quantum dynamical control under varying coupling strengths. Our results reveal fundamental constraints and opportunities in quantum thermometry, offering practical strategies for the design of high-performance quantum thermometers operating in realistic open quantum systems.
Quantum thermometry aims to measure temperature in nanoscale quantum systems, paralleling classical thermometry. However, temperature is not a quantum observable, and most theoretical studies have therefore concentrated on analyzing fundamental precision limits set by the quantum Fisher information through the quantum Cramer-Rao bound. In contrast, whether a direct temperature readout can be achieved in quantum thermometry remains largely unexplored, particularly under the nonequilibrium conditions prevalent in real-world applications. To address this, we develop a direct temperature readout scheme based on a thermodynamic inference strategy. The scheme integrates two conceptual developments: (i) By applying the maximum entropy principle with the thermometer's mean energy as a constraint, we assign a reference temperature to the nonequilibrium thermometer. We demonstrate that this reference temperature outperforms a commonly used effective temperature defined through equilibrium analogy. (ii) We obtain positive semi-definite error functions that lower-bound the deviation of the reference temperature from the true temperature-in analogy to the quantum Cramer-Rao bound for the mean squared error-and vanish upon thermalization with the sample. Combining the reference temperature with these error functions, we introduce a notion of corrected dynamical temperature which furnishes a postprocessed temperature readout under nonequilibrium conditions. This corrected dynamical temperature can be evaluated adaptively without prior knowledge of the actual temperature. We validate the corrected dynamical temperature in a qubit-based thermometer under a range of nonequilibrium initial states, confirming its capability to estimate the true temperature. Importantly, we find that increasing quantum coherence can enhance the precision of this readout.
We investigate the sensing performance of a single-qubit quantum thermometer within a non-Markovian dynamical framework. By employing an exactly numerical hierarchical equations of the motion method, we go beyond traditional paradigms of the Born-Markov theory, the pure dephasing mechanism, and the weak-coupling approximation, which were commonly used in many previous studies of quantum thermometry. We find (i) the non-Markovian characteristics may boost the estimation efficiency, (ii) the sensitivity of quantum thermometry can be effectively optimized by engineering the proportions of different coupling operators in the whole sensor-reservoir interaction Hamiltonian, and (iii) a threshold, above which the strong sensor-reservoir coupling can significantly enhance the sensing precision in the long-encoding-time regime. Our results may have certain applications for high-resolution quantum thermometry.
Quantum thermometry based on single-qubit sensor configurations enables the precise estimation of the temperature of a cosmological Anti-de Sitter (AdS) spacetime. In this work, we characterize the achievable estimation accuracy using the Quantum Fisher Information (QFI) and the associated quantum signal-to-noise ratio. For the first time, we introduce an ancillary Unruh-DeWitt detector between the sensor and the thermal bath, enhancing thermometric sensitivity by channeling temperature-dependent information into the probe qubit's coherence. We examine how detector acceleration in AdS space and the choice of boundary conditions modify the probe's thermal sensitivity. Despite the differing geometries, a unified phenomenology emerges: we characterize the scaling of the QFI with respect to temperature, detector energy gap, spacetime curvature, and interaction time. Finally, we identify optimal state preparation and measurement strategies that maximize the QFI, thereby establishing the fundamental limits of precision for non-Markovian sensing in curved spacetime.
The rapidly developing quantum technologies and thermodynamics have put forward a requirement to precisely control and measure the temperature of microscopic matter at the quantum level. Many quantum thermometry schemes have been proposed. However, precisely measuring low temperature is still challenging because the obtained sensing errors generally tend to diverge with decreasing temperature. Using a continuous-variable system as a thermometer, we propose non-Markovian quantum thermometry to measure the temperature of a quantum reservoir. A mechanism to make the sensing error $\ensuremath{\delta}T$ scale with the temperature T as the Landau bound $\ensuremath{\delta}T\ensuremath{\simeq}T$ in the full-temperature regime is discovered. Our analysis reveals that it is the quantum criticality of the total thermometer-reservoir system that causes this enhanced sensitivity. Efficiently avoiding the error-divergence problem, our result gives an efficient way to precisely measure the low temperature of quantum systems.
Accurate temperature estimation in the quantum and cryogenic regimes remains a fundamental challenge. Here, we investigate nonequilibrium quantum thermometry using a single-qubit probe coupled to a bosonic bath through noncommuting interaction operators, which unify pure dephasing and dissipative dynamics within a spin-boson model. We show that the interference between these two coupling channels induces strong non-Markovian feedback between populations and coherences, leading to coherence trapping and enhanced thermal sensitivity. Remarkably, by tuning the coupling structure, the probe's temperature sensitivity exhibits a quadratic low-temperature scaling, even under weak coupling. Moreover, while coherence-based measurements are formally suboptimal, they become the most informative in the early nonequilibrium regime, where memory effects dominate. Our findings identify noncommutative system-bath couplings as a practical and tunable resource for achieving high-precision quantum thermometry in realistic open-system architectures.