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.
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.
We investigate a nonequilibrium quantum thermometry protocol in which an ensemble of qubits, acting as temperature probes, is weakly coupled to a macroscopic thermal bath. The temperature of the bath, the parameter of interest, is encoded in the dissipator of a Markovian thermalization process. For some relevant initial states, we observe a peak in the Quantum Fisher Information (QFI) during the transient of the thermalization, indicating enhanced sensitivity in early-time dynamics. This effect becomes more pronounced at higher bath temperatures and is further enhanced when the initial reduced state of the qubits has a large ground-state population and/or it is highly coherent. We also focus on the role of initial quantum correlations in the thermometric performance, which emerge as a central feature of this work. We find strong numerical evidence that, given same single-qubit reduced states, the inclusion of quantum correlations among the qubits of the ensemble always yields an enhanced QFI. Moreover, even if none of the considered states outperform the (pure, separable) ground state, maximally entangled states display QFIs values remarkably close to the standard quantum limit when probing extremely hot thermal baths. Finally, although the Markovian dynamics does not permit superlinear scaling of the QFI with the number of probes, we identify the most effective initial states for designing high-precision quantum thermometers within this setting. We also provide concrete guidelines for experimental implementations.
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.
We unveil a fundamental temperature bias in transient quantum thermometry under Markovian dynamics. For qubit probes evolving in a thermal Markovian environment, we prove that transient precision beyond the steady-state benchmark can be achieved if and only if the probe is initially colder than the bath temperature to be estimated. Cold probes are therefore both necessary and sufficient for enhanced transient precision in the Markovian regime. We then investigate the fate of this bias in the presence of environmental memory. In particular, in a non-Markovian scenario generated by an auxiliary-mediated system-bath coupling, we find that the cold-probe requirement for enhanced transient precision persists, indicating that the temperature bias survives certain forms of memory effects. In contrast, for a non-Markovian collisional model with perfect swap interactions between bath ancillas, transient enhancement is entirely absent regardless of the probe's initial temperature. This indicates that strong non-Markovianity can lead to the complete disappearance of the enhancement effect, placing hot and cold probes on equal footing, with neither capable of achieving enhanced precision in this regime.
We address a particular instance where open quantum systems may be used as quantum probes for an emergent property of a complex system, as the temperature of a thermal bath. The inherent fragility of the quantum probes against decoherence is the key feature making the overall scheme very sensitive. The specific setting examined here is that of quantum thermometry, which aims to exploit decoherence as a resource to estimate the temperature of a sample. We focus on temperature estimation for a bosonic bath at equilibrium in the Ohmic regime (ranging from sub-Ohmic to super-Ohmic), by using pairs of qubits in different initial states and interacting with different environments, consisting either of a single thermal bath or of two independent ones at the same temperature. Our scheme involves pure dephasing of the probes, thus avoiding energy exchange with the sample and the consequent perturbation of temperature itself. We discuss the role of correlations among the probes and the presence of a local versus a global bath. We show that entanglement improves thermometry at short times if the two qubits are embedded in a common bath, whereas if the interaction time is not constrained, then coherence rather than entanglement is the key resource in quantum thermometry.
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.
We study low-temperature non-equilibrium quantum thermometry with a bosonic probe: a quantum harmonic oscillator strongly coupled to a bosonic bath at temperature T through a Drude--Ohmic spectral density. We treat the probe--bath dynamics both exactly, using the quadratic solution of Boyanovsky and Jasnow, and within a renormalized Gorini--Kossakowski--Lindblad--Sudarshan (GKLS) master equation. From the time-dependent covariance matrix we extract the quantum Fisher information (QFI) for general single-mode Gaussian probe states, including squeezed ones. In the strong-coupling, non-Markovian regime the QFI is non-monotonic in time, displaying bath-memory revivals that make a finite interrogation time t∗>0 strictly optimal. By contrast, we prove that the Markovian QFI rises monotonically to its stationary value and develops no interior optimum, so that its optimum is always pinned to the boundary t∗→∞; this complements existing Markovian precision-rate bounds, which concern (F(t)/t) rather than the single-shot QFI (F(t)). Squeezed initial states yield a large transient advantage that thermalisation eventually erases, establishing squeezing and interrogation time as complementary thermometric resources. At equilibrium, strong coupling replaces the exponential Boltzmann suppression of the low-temperature relative error by a far milder polynomial divergence. As the model maps directly onto circuit quantum electrodynamics, these protocols appear within current experimental reach.