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Physical Review Research

Enhancement of quantum sensing by noncanonical effects

S. Y. Li, Qing-Shou Tan, Wei Wu

Published Jun 6, 2025• 5 citations
Publisher

Abstract

Equilibrium probes have been widely used in various schemes of sensing to quantum reservoirs. Many previous studies assumed that the probe-reservoir coupling is sufficiently weak such that the equilibrium state of the probe is approximately described by a canonical Gibbs state at the same temperature of the reservoir. Such a weak-coupling approximation severely restricts the range of application for an equilibrium-probe-based quantum sensing scenario. Going beyond the weak-coupling limitation, we here investigate the noncanonical effect, which is naturally induced by strong couplings, on the performance of a quantum sensing scheme. In this scheme, a quantum two-level system is used as the probe to estimate the parameters of a dissipative bosonic reservoir, by employing the polaron transformation approach. It is found that, compared with that of the canonical-equilibrium-state case, the noncanonical effect can effectively boost the sensing precision at both zero and finite temperatures. Paving the way toward realizing high-precision quantum sensing in practice, our result reveals the positive role of noncanonicality in the studies of quantum technologies.

DOI
10.1103/physrevresearch.7.023235

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Equilibrium probes have been widely used in various schemes of sensing to quantum reservoirs. Many previous studies assumed that the probe-reservoir coupling is sufficiently weak such that the equilibrium state of the probe is approximately described by a canonical Gibbs state at the same temperature of the reservoir. Such a weak-coupling approximation severely restricts the range of application for an equilibrium-probe-based quantum sensing scenario. Going beyond the weak-coupling limitation, we here investigate the noncanonical effect, which is naturally induced by strong couplings, on the performance of a quantum sensing scheme. In this scheme, a quantum two-level system is used as the probe to estimate the parameters of a dissipative bosonic reservoir, by employing the polaron transformation approach. It is found that, compared with that of the canonical-equilibrium-state case, the noncanonical effect can effectively boost the sensing precision at both zero and finite temperatures. Paving the way toward realizing high-precision quantum sensing in practice, our result reveals the positive role of noncanonicality in the studies of quantum technologies.
Equilibrium probes have been widely used in various noisy quantum metrology schemes. However, such an equilibrium-probe-based metrology scenario severely suffers from the low-temperature-error-divergence problem in the weak-coupling regime. To circumvent this limit, we propose a strategy to eliminate the error-divergence problem by utilizing the strong-coupling effects, which can be captured by the reaction-coordinate mapping. The strong couplings induce a noncanonical equilibrium state which greatly enhances the metrology performance. It is found that our metrology precision behaves as a polynomial-type scaling relation, which suggests the reduction of temperature can be used as a resource to improve the metrology performance. Our result is sharply contrary to that of the weak-coupling case, in which the metrology precision exponentially decays as the temperature decreases. Paving a way to realize a high-precision noisy quantum metrology at low temperatures, our result reveals the importance of the non-Markovianity in quantum technologies.
Abstract Criticality is widely regarded as a potential resource to boost the performance of quantum sensing. In existing protocols of criticality-enhanced quantum sensing, the criticality typically originates either from the probe or from the detected system itself. We here propose a scheme for sensing a dissipative reservoir based on the thermal criticality induced by the probe-reservoir interaction at finite temperature. It is revealed that the strong-coupling characteristics of the probe are able to create an additional thermal criticality, which significantly enhances the sensing performance. Our proposed scheme does not require precise dynamical control and is universal to different initial states, as it is built upon the equilibrium state generated by the natural dissipative dynamics of the probe. Expanding the scope of critical metrology, our findings pave a possible route toward high-precision quantum sensing.
We investigate the non-monotonic temperature sensitivity of a coherently driven two-level quantum system coupled to an Ohmic phonon environment. By employing a unitary polaron transformation, we account for phonon-induced renormalization effects that go beyond the standard weak-coupling approximations. Our analysis reveals that the Quantum Fisher Information (QFI) exhibits a prominent peak at an intermediate system-environment coupling strength, identifying an optimal regime for thermal sensing. This behavior emerges from a fundamental competition between environment-induced dissipation enhancement and the exponential suppression of system parameters due to phonon dressing. We demonstrate that while thermometric precision vanishes in both the ultra-weak and strong coupling limits, a properly tuned nonequilibrium steady state can significantly enhance sensitivity. These results suggest that environmental interactions, often viewed as detrimental decoherence sources, can be engineered as a resource to optimize the performance of solid-state quantum thermometers.
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.
In many previous temperature estimation schemes, the temperature of a sample is directly read out from the final steady state of a quantum probe, which is coupled to the sample. However, in these studies, information of correlations between system (the probe) and reservoir (the sample) is usually eliminated, leading the steady state of the probe is a canonical equilibrium state with respect solely to system’s Hamiltonian. To explore the influence of system–reservoir correlations on the estimation precision, we investigate the equilibration dynamics of a spin interacting with a finite temperature bosonic reservoir. By incorporating an intermediate harmonic oscillator or a collective coordinate into the spin, the system–reservoir correlations can be correspondingly encoded in a Gibbs state of an effective Hamilton, which is size consistent with the original bare spin. Extracting information of temperature from this corrected steady state, we find the effect of the system-reservoir correlations on the estimation precision is highly sensitive to the details of the spectral density function of the measured reservoir.
Abstract Quantum probing is the art of exploiting simple quantum systems interacting with a complex environment to extract precise information about some environmental parameters, e.g. the temperature of the environment or its spectral density. Here we analyze the performance of a single-qubit probe in characterizing Ohmic bosonic environments at thermal equilibrium. In particular, we analyze the effects of tuning the interaction Hamiltonian between the probe and the environment, going beyond the traditional paradigm of pure dephasing. In the weak-coupling and short-time regime, we address the dynamics of the probe analytically, whereas numerical simulations are employed in the strong coupling and long-time regime. We then evaluate the quantum Fisher information for the estimation of the cutoff frequency and the temperature of the environment. Our results provide clear evidence that pure dephasing is not optimal, unless we focus attention to short times. In particular, we found several working regimes where the presence of a transverse interaction improves the maximum attainable precision, i.e. it increases the quantum Fisher information. We also explore the role of the initial state of the probe and of the probe characteristic frequency in determining the estimation precision, thus providing quantitative guidelines to design optimized detection to characterize bosonic environments at the quantum level.