A dephasing qubit can sense temperature through its loss of coherence, but the same signal also depends on the strength of its coupling to the sample. We determine the high-temperature cost of estimating temperature when the spectral amplitude is unknown in an exactly solvable Ohmic model with an exponential cutoff. For independent, freely timed interrogations, the optimized effective Fisher information per shot is asymptotic to 0.00612330 a⁻² T⁻⁸, whereas the calibrated benchmark is 0.161903 T⁻². With total sensing time as the resource and zero reset overhead, the corresponding powers are T−15/2 and T−3/2. The six-power separation results from near-collinearity of the temperature and coupling scores: the leading thermal correction changes their common amplitude before a smaller time-dependent contribution distinguishes them. We prove an upper bound over all interrogation-time allocations and construct a two-time design attaining its leading constant. Arbitrary-precision calculations, independent integral evaluation, and synthetic counting experiments check the analytic and statistical calculations. We also identify the scale of independent calibration information required to compete with the uncalibrated signal. The conclusions are local estimation bounds for a fixed spectral model and a fixed positive coupling amplitude; they do not establish an adaptive protocol or an advantage over other thermometers.
A dephasing qubit can sense temperature through its loss of coherence, but the same signal also depends on the strength of its coupling to the sample. We determine the high-temperature cost of estimating temperature when the spectral amplitude is unknown in an exactly solvable Ohmic model with an exponential cutoff. For independent, freely timed interrogations, the optimized effective Fisher information per shot is asymptotic to 0.00612330 a⁻² T⁻⁸, whereas the calibrated benchmark is 0.161903 T⁻². With total sensing time as the resource and zero reset overhead, the corresponding powers are T−15/2 and T−3/2. The six-power separation results from near-collinearity of the temperature and coupling scores: the leading thermal correction changes their common amplitude before a smaller time-dependent contribution distinguishes them. We prove an upper bound over all interrogation-time allocations and construct a two-time design attaining its leading constant. Arbitrary-precision calculations, independent integral evaluation, and synthetic counting experiments check the analytic and statistical calculations. We also identify the scale of independent calibration information required to compete with the uncalibrated signal. The conclusions are local estimation bounds for a fixed spectral model and a fixed positive coupling amplitude; they do not establish an adaptive protocol or an advantage over other thermometers.
We investigate the quantum sensing performance of a dephasing qubit as a probe in Ohmic environments, characterized by the coupling strength η, the Ohmicity parameter s, and the cutoff frequency ωc to be estimated. The performance is quantified by the dimensionless quantum signal-to-noise ratio Q. We show that the evolution of Q with the scaled time ωct is independent of ωc, and peaks at an optimal time topt, yielding optimal sensitivity Qopt. We analyze how Qopt depends on η, s and the temperature T. Our results demonstrate that, for any Ohmic environment, provided that ωctopt≪1, Qopt always reaches the upper bound: Qmax=0.648 at zero temperature, and consistently attains Qmax/4 at high temperatures. Remarkably, we find that increasing the scaled temperature T/ωc can enhance Qopt by nearly two orders of magnitude compared to its zero-temperature counterpart for certain Ohmic environments. Our work reveals that temperature can serve as a resource to enhance sensing precision, as it accelerates the encoding of the cutoff frequency information into the probe state, thereby enabling optimal measurement within a short time window.
We investigate quantum thermometry in Ohmic-type reservoirs using two-qubit probes within an exactly solvable pure-dephasing framework. By analyzing the individual variance associated with temperature estimation, we identify optimal regimes governed by the Ohmicity parameter s, the deviation angle θ, and the decay coefficients α and β, thereby determining the conditions that minimize estimation errors. The Quantum Fisher Information (QFI) exhibits pronounced maxima at finite interaction times, especially in sub-Ohmic and Ohmic environments at low temperatures, whereas super-Ohmic reservoirs flatten the QFI peak and shift the optimal sensitivity toward higher temperatures. Consistently, the quantum signal-to-noise ratio (QSNR) is suppressed at low temperatures, increases with thermal excitation, and saturates in the high-temperature regime, where the influence of spectral details becomes negligible. A comparative study of mutual and local estimation strategies shows that common-bath configurations, particularly for Σ+ and Σ0 probes, outperform local baths at short interaction times due to bath-induced correlations, while local environments become advantageous at longer times. The analysis further reveals finite optimal values of both the interaction time topt and the temperature Topt, as well as a strong reduction of the variance with increasing measurement number in the low-temperature regime. In addition, our study of hyperon-antihyperon channels (Λ, Σ+, Σ0, Ξ−, Ξ0) shows that entanglement and quantum discord remain remarkably robust over broad angular domains, whereas steering and Bell nonlocality are confined to narrower regions. Overall, the interplay between spectral structure, particle-dependent parameters, and estimation strategy provides valuable ...
We investigate the dephasing dynamics of a qubit as an effective mechanism for estimating the temperature of its surrounding environment for different symmetries. Our approach is fundamentally quantum, leveraging the qubit’s susceptibility to decoherence without necessitating thermal equilibrium with the system under study. We also examine how symmetry properties affect the accuracy of information retrieval and the robustness of quantum information storage in such systems, highlighting their potential advantages in mitigating decoherence effects. The optimization of quantum Fisher information is performed with respect to both the interaction duration and the environmental temperature, focusing on Ohmic-like spectral density environments. Furthermore, we explicitly identify the optimal qubit measurement that attains the quantum Cramér–Rao bound for precision. Our findings reveal that optimal estimation arises from a complex interplay between the qubit’s dephasing dynamics and the Ohmic characteristics of the environment, with a particular focus on non-Hermitian systems that exhibit enhanced resilience to decoherence. We examine the decoherence dynamics of a two-level spin system governed by an anti-parity-time-symmetric Hamiltonian. The obtained results are systematically compared with those corresponding to both PT-symmetric and conventional Hermitian qubit models. To this end, we first employ a time-dependent Dyson transformation to derive the exact analytical evolution of a generic non-Hermitian qubit interacting with an external environment. The formalism is then applied to the particular case of an anti-PT-symmetric qubit. Our analysis reveals that the coherence of the non-Hermitian-symmetric qubit is preserved over significantly longer times, as evidenced by the slower decay of its decoherence function relative to its Hermitian counterparts. Furthermore, the generation of entanglement entropy is found to proceed at a reduced rate, indicating a more gradual buildup of system–environment correlations. In addition, the anti-PT-symmetric configuration exhibits substantially enhanced quantum Fisher information together with a smaller variance than those observed in the corresponding PT-symmetric and Hermitian systems. These findings highlight the remarkable robustness of anti-PT-symmetric qubits against environmental decoherence and suggest that they constitute a promising platform for the implementation of quantum information processing and quantum computing protocols.
Quantum thermometry aims at determining temperature with ultimate precision in the quantum regime. Standard equilibrium approaches, limited by the Quantum Fisher Information given by static energy fluctuations, lose sensitivity outside a fixed temperature window. Non-equilibrium strategies have therefore been recently proposed to overcome these limits, but their advantages are typically model-dependent or tailored for a specific purpose. This Letter establishes a general, model-independent result showing that any temperature-dependent unitary driving applied to a thermalized probe enhances its quantum Fisher information with respect to its equilibrium value. Such information gain is expressed analytically through a positive semi-definite kernel of information currents that quantify the flow of statistical distinguishability. Our results, together with an analysis of the relation between information gain and control cost, are benchmarked on a driven spin-1/2 thermometer, furthermore showing that resonant modulations remarkably restore the quadratic-in-time scaling of the Fisher information and allow to shift the sensitivity peak across arbitrary temperature ranges.
One of the main advantages expected from using quantum probes as thermometers is noninvasiveness, i.e., a negligible perturbation to the thermal sample. However, invasiveness is rarely investigated explicitly. Here, focusing on a spin probe undergoing pure dephasing due to the interaction with a bosonic sample, we show that there is a nontrivial relation between the information on the temperature gained by a quantum probe and the heat absorbed by the sample due to the interaction. We show that time-optimal probing schemes obtained by considering the total experiment time as a resource also have the benefit of limiting the heat absorbed by the sample in each shot of the experiment. For such time-optimal protocols, we show that it is advantageous to have strong probe-sample coupling, since in this regime the accuracy increases linearly with the coupling strength, while the amount of heat per shot saturates to a finite value. Since in pure-dephasing models the absorbed heat corresponds to the external work needed to couple and decouple the probe and the sample, our results also represent a first step towards the analysis of the thermodynamic and energetic cost of 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.