Quantum criticality, as a fascinating quantum phenomenon, may provide significant advantages for quantum sensing. Here we propose a dynamic framework for quantum sensing with a family of Hamiltonians that undergo quantum phase transitions (QPTs). By giving the formalism of the quantum Fisher information (QFI) for quantum sensing based on critical quantum dynamics, we demonstrate its divergent feature when approaching the critical point. We illustrate the basic principle and the details of experimental implementation using quantum Rabi model. The framework is applicable to a variety of examples and does not rely on the stringent requirement for particular state preparation or adiabatic evolution. It is expected to provide a route towards the implementation of criticality-enhanced quantum sensing.
Quantum criticality, as a fascinating quantum phenomenon, may provide significant advantages for quantum sensing. Here we propose a dynamic framework for quantum sensing with a family of Hamiltonians that undergo quantum phase transitions (QPTs). By giving the formalism of the quantum Fisher information (QFI) for quantum sensing based on critical quantum dynamics, we demonstrate its divergent feature when approaching the critical point. We illustrate the basic principle and the details of experimental implementation using quantum Rabi model. The framework is applicable to a variety of examples and does not rely on the stringent requirement for particular state preparation or adiabatic evolution. It is expected to provide a route towards the implementation of criticality-enhanced quantum sensing.
Quantum Fisher information (QFI) may exhibit the irregular behavior at the critical point of phase transitions of a physical system and be very sensitive to slight variations of some controlling parameters. This parameter sensitivity may be used for quantum parameter estimation or quantum sensing. In this study, taking the quantum Rabi model as an example, we investigate the critical properties of the QFI for the parameter estimation at the critical point of the SU(1,1) dynamic systems. We show that the QFI goes divergently in the sixth power law (T6) of the parameter coding time around the critical point. After taking into the consumption of energy during the dynamic evolution, we find that the variation of the QFI around the critical point is scaled by the Heisenberg scaling T2. It is noticed that for nonclassical initial probe states the scaling of QFI can beat the standard quantum limit (n0) as a function of the initial mean phonon number n0. The homodyne and phonon-number measurement schemes are compared. We find that the quantum Cram\'er-Rao bound can be reached by use of the phonon-number detection scheme. However, it is more sensitive to the noise than the homodyne detection scheme. We extend the investigation to a two-mode non-Hermitian system and show that the QFI exhibits the same irregular properties at the exceptional point, revealing that for the SU(1,1) dynamic systems the QFI universally diverges as T6 at the critical point.
Critical properties of a quantum system are recognized as valuable resources for quantum metrology. In this work, we investigate the criticality-enhanced sensing in a quantum Rabi triangle system, which exhibits multiple phases. Around the phase boundary, enhanced parameter estimation precision can be achieved by tuning either the scaled coupling strength or the hopping phase controlled by an artificial magnetic field. We observe that the quantum Fisher information shows divergent scaling near different quantum phase transition points, characterized by distinct critical exponents. When the resource consumption is taken into account, we find that the divergent quantum Fisher information can reach the Heisenberg limit. Furthermore, we propose a measurement scheme of the average photon number and the quantum Cramér-Rao bound can be saturated.
We use the quantum Fisher information (QFI) to diagnose a dynamical phase transition (DPT) in a closed quantum system, which is usually defined in terms of nonanalytic behavior of a time-averaged order parameter. Employing the Lipkin-Meshkov-Glick model as an illustrative example, we find that the DPT correlates with a peak in the QFI that can be explained by a generic connection to an underlying excited-state quantum phase transition that also enables us to relate the scaling of the QFI with the behavior of the order parameter. Motivated by the QFI as a quantifier of metrologically useful correlations and entanglement, we also present a robust interferometric protocol that can enable DPTs as a platform for quantum-enhanced sensing.
Quantum-enhanced sensing is commonly benchmarked using the quantum Fisher information (QFI), often interpreted as a direct indicator of achievable precision. However, such an interpreta- tion is only justified within a fully specified inference framework that consistently incorporates state preparation, measurement design, resource accounting, estimator construction, prior information, and finite data effects. Here we develop an operational, end-to-end framework for quantum sensing under finite resources and identify general principles required for meaningful performance assess- ment. A central conceptual point is that the relevant unit of estimation is not a single detection event, but the complete data set required to construct a consistent estimator. Rather than relying on abstract statistical formalism, we analyze a set of paradigmatic and experimentally relevant ex- amples that expose common pitfalls in widely discussed quantum sensing strategies. These include quantum interferometry, sensing with squeezed states, and criticality-inspired protocols. Our results clarify when large Fisher information or nonclassical resources translate into genuine metrological advantage, and when they do not. They further provide a practical methodology for designing and evaluating quantum sensing protocols under realistic experimental constraints.
Critical quantum metrology exploits the dramatic growth of the quantum Fisher information near quantum phase transitions to enhance the precision of parameter estimation. This enhancement is commonly associated with a closing energy gap, which causes the characteristic timescales for adiabatic preparation or relaxation to diverge with increasing system size. As a consequence, the apparent growth of the quantum Fisher information largely reflects the increasing evolution time induced by critical slowing down rather than a genuine improvement in metrological performance, thereby limiting the practical usefulness of such protocols. Here we show that the relationship between energy gaps, quantum correlations, and achievable precision in interacting quantum systems can be far more subtle. In particular, quantum-enhanced sensitivity can also emerge when the energy gap increases, eliminating critical slowing down and enabling substantially faster relaxation dynamics. Although the corresponding quantum Fisher information may decrease due to the shorter evolution time, the resulting precision can nevertheless remain quantum-enhanced. Building on this insight, we introduce an anti-critical quantum metrology scheme in which quantum-enhanced precision arises while the energy gap grows. We illustrate this mechanism using the quantum Rabi model, thereby identifying a route to metrological advantage that avoids the slow dynamics associated with conventional criticality.
The aging transition is a critical phenomenon in which collective dynamics deteriorate as the fraction of inactive quantum nodes exceeds a threshold, referred to as the aging transition point. Such transitions are relevant to a broad range of biological and physiological systems, and may play an important role in quantum information processing, particularly in the stability assessment and robustness control of quantum networks. Detecting the aging transition point is therefore crucial for predicting network breakdown, since it marks the critical threshold at which a quantum network abruptly loses its stable active state and enters a degraded inactive phase. Here we propose a quantum sensing strategy to locate this transition point using a single qubit probe coherently coupled to a small subset of oscillator nodes. As the inactive fraction p approaches the aging transition point, the excited-state population of the probe becomes highly sensitive to variations in p, leading to a pronounced enhancement of the Fisher information. This critical enhancement enables high-precision estimation of the transition point. Remarkably, this enhancement survives even in the classical regime for the oscillators, where the Fisher information increases dramatically as p approaches the transition region. Our results establish a feasible route to sensing aging transitions in oscillator networks and provide a metrological perspective on critical phenomena in quantum many-body systems.