Central to non-Hermitian sensing is the question of whether exceptional points (EPs) can make weak perturbations easier to detect. We show that despite enhanced spectral response, in finite-dimensional Lindblad systems with a unique stationary state and a nonzero relaxation gap, EPs offer no fundamental advantage in how the observation time required for reliable detection of a weak perturbation scales with the perturbation strength. We nevertheless demonstrate that by selectively choosing perturbations that enhance the quantum Fisher information rate, EPs can shorten the observation time needed to reach a predefined detection accuracy relative to a comparable non-EP reference at the same decay rate. As an illustration, we show using an optomechanical model at an EP that we can detect a weak force through the cavity output at the same reliability in less time than a non-EP reference. Our results establish fundamental limits on perturbation detection at EPs and can guide the design of faster non-Hermitian sensors based on optomechanical resonators, superconducting qubits, and trapped ions.
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The paper asks whether enhanced spectral sensitivity at Liouvillian exceptional points (EPs) reduces the observation time needed to distinguish a weak perturbation from its absence. It formulates equal-prior binary discrimination with arbitrary measurements on the sensor and all emitted fields, relating optimal success probability to their joint-state overlap.
For finite-dimensional Lindblad systems with analytic parameter dependence, a unique stationary state and a uniform nonzero relaxation gap, an analytic eigenvalue of a two-sided overlap generator controls long-time distinguishability. This gives $P^\star=(1+\sqrt{1-e^{-f_Q\delta^2T/4}})/2+o(1)$, where $f_Q$ is the quantum Fisher information rate. For $f_Q>0$, fixed detection reliability requires $T\propto\delta^{-2}$. On the inverse-splitting timescale of a generic order-$m$ EP, $T\sim|\delta|^{-1/m}$, optimal success instead tends to $1/2$.
For Hamiltonian perturbations restricted to a real $m$-dimensional coalescing decay block, integrating stationary correlations yields an exact balance: relative to a simple-exponential reference with matching stationary statistics and decay rate, the information gain satisfies $\overline{\mathcal E}=1$ and $0\leq\mathcal E\leq m$. Selected perturbations can therefore reduce asymptotic detection time by at most a factor $m$, while others lose sensitivity.
A vacuum, linearized optomechanical EP2 model illustrates this selectivity: ideal cavity-output collection gives a force-detection time about $49.85\%$ shorter than the specified reference oscillator. The force does not split the EP. The comparison is not a universal advantage over non-EP sensors; the example is infinite-dimensional and outside the general proof, assumes vacuum baths and known force phase, and its gain depends on collection efficiency.
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Central to non-Hermitian sensing is the question of whether exceptional points (EPs) can make weak perturbations easier to detect. We show that despite enhanced spectral response, in finite-dimensional Lindblad systems with a unique stationary state and a nonzero relaxation gap, EPs offer no fundamental advantage in how the observation time required for reliable detection of a weak perturbation scales with the perturbation strength. We nevertheless demonstrate that by selectively choosing perturbations that enhance the quantum Fisher information rate, EPs can shorten the observation time needed to reach a predefined detection accuracy relative to a comparable non-EP reference at the same decay rate. As an illustration, we show using an optomechanical model at an EP that we can detect a weak force through the cavity output at the same reliability in less time than a non-EP reference. Our results establish fundamental limits on perturbation detection at EPs and can guide the design of faster non-Hermitian sensors based on optomechanical resonators, superconducting qubits, and trapped ions.
The paper asks whether enhanced spectral sensitivity at Liouvillian exceptional points (EPs) reduces the observation time needed to distinguish a weak perturbation from its absence. It formulates equal-prior binary discrimination with arbitrary measurements on the sensor and all emitted fields, relating optimal success probability to their joint-state overlap.
For finite-dimensional Lindblad systems with analytic parameter dependence, a unique stationary state and a uniform nonzero relaxation gap, an analytic eigenvalue of a two-sided overlap generator controls long-time distinguishability. This gives P⋆=(1+1−e−fQδ2T/4)/2+o(1), where fQ is the quantum Fisher information rate. For fQ>0, fixed detection reliability requires T∝δ−2. On the inverse-splitting timescale of a generic order-m EP, T∼∣δ∣−1/m, optimal success instead tends to 1/2.
For Hamiltonian perturbations restricted to a real m-dimensional coalescing decay block, integrating stationary correlations yields an exact balance: relative to a simple-exponential reference with matching stationary statistics and decay rate, the information gain satisfies E=1 and 0≤E≤m. Selected perturbations can therefore reduce asymptotic detection time by at most a factor m, while others lose sensitivity.
A vacuum, linearized optomechanical EP2 model illustrates this selectivity: ideal cavity-output collection gives a force-detection time about 49.85% shorter than the specified reference oscillator. The force does not split the EP. The comparison is not a universal advantage over non-EP sensors; the example is infinite-dimensional and outside the general proof, assumes vacuum baths and known force phase, and its gain depends on collection efficiency.
Exceptional points (EPs) exhibit strongly enhanced spectral responses and are therefore promising candidates for sensing applications. Whether these non-Hermitian degeneracies provide a genuine advantage in the quantum regime has been the subject of ongoing debate. Here, we address this issue within a scattering-matrix formalism for sensing with coherent light, which allows the quantum Fisher information (QFI) to be evaluated directly from experimentally accessible scattering data without introducing additional noise channels beyond those inherent to the scattering process. We analyze both nondegenerate and degenerate scattering-matrix poles, including EPs of arbitrary order, and show that the QFI per incoming photon flux is governed by three key factors: the decay rate of the resonant mode, the strength of the spectral response associated with non-normality, and the adjustment between the scattering states and the information source. For spatially localized perturbations, this implies that the Fisher information is fully determined by the local density of states at the perturbation site. Within this framework, we demonstrate that EPs can enhance the QFI compared to isolated modes or diabolic points with identical decay rates, and that the QFI can be further increased by moving away from the EP toward parameter regimes where non-Hermitian linewidth splitting reduces the decay rate of one mode. We further show that sufficiently small additional internal losses do not alter this overall picture, thereby providing a unified and experimentally relevant perspective on the design of quantum-limited non-Hermitian sensors.
Abstract Exceptional points (EPs) of the effective non-Hermitian Hamiltonian and of the Liou- villian superoperator are often treated interchangeably in dissipative quantum sensing. In the exactly solvable amplitude-damped two-level sensor we prove that the two degeneracies live at different parameter points—the Hamiltonian EP at (ε,∆) = (0,γ/2), where the Li- ouvillian spectrum is perfectly regular, and the genuine Liouvillian EP at (0,γ/4), where a Jordan block appears—and derive the closed-form stationary quantum Fisher informa- tion (QFI), finite at both EPs and globally maximized at a non-EP point. The divergent response motivating EP sensing lives exclusively in the no-jump (post-selected) sector, at a post-selection success cost that vanishes linearly with the detuning. We classify Liouvil- lian EPs into gap-closing (type I, genuine critical resources) and finite-rate (type II, not resources), validated by a degenerate parametric oscillator, and benchmark the stationary results against the scattering-matrix QFI bound of Wiersig and Rotter (enhancement factor 4 reproduced). Forstationarydissipativesensors, neitherEPalonegrantsQFIenhancement.
Exceptional points (EPs) can induce strongly amplified responses to weak perturbations, but enhanced spectral sensitivity in conventional non-Hermitian systems does not necessarily translate into improved quantum-limited sensing because of the associated gain and loss noise. Here, we investigate a tunable EP sensing platform based on the intrinsic non-Hermitian Bogoliubov dynamics of a spin-orbit-angular-momentum-coupled Bose-Einstein condensate. Starting from a fully Hermitian microscopic Hamiltonian, we derive a Bogoliubov dynamical matrix that exhibits parity-time (PT) symmetry, with EPs tunable through the Raman coupling and interaction parameters. We identify multiple EPs and map their trajectories and associated stability landscapes, revealing strong quantum Fisher information enhancement when the EPs are approached from the PT-symmetric stable regime. We further find that the gap-opening rate around a second-order EP provides a useful relative indicator for comparing the sensing performance of EPs, while higher-order EPs are not necessarily accessible from the stable regime. Moreover, two second-order EPs can be tuned to overlap, allowing their sensing contributions to add and yielding a linear enhancement of the total quantum Fisher information. Finally, we show that a spin-density measurement can approach the quantum Fisher information limit, providing an experimentally accessible route to tunable EP-enhanced quantum sensing in Bose-Einstein condensates.
Open quantum systems can have exceptional points (EPs), degeneracies where both eigenvalues and eigenvectors coalesce. Recently, it has been proposed and demonstrated that EPs can enhance the performance of sensors in terms of amplification of a detected signal. However, typically amplification of signals also increases the system noise, and it has not yet been shown that an EP sensor can have improved signal-to-noise performance. We develop a quantum noise theory to calculate the signal-to-noise performance of an EP sensor. We use the quantum Fisher information to extract a lower bound for the signal-to-noise ratio (SNR) and show that parametrically improved SNR is possible. Finally, we construct a specific experimental protocol for sensing using an EP amplifier near its lasing threshold and heterodyne signal detection that achieves the optimal scaling predicted by the Fisher bound. Our results can be generalized to higher order EPs for any bosonic non-Hermitian system with linear interactions.
ABSTRACT Exceptional points (EPs), singularities in non‐Hermitian systems where eigenvalues and eigenstates coalesce, exhibit unique spectral responses and enhanced sensitivity. However, in quantum‐interference settings such as two‐photon measurements, the interference transition generally does not occur at the EPs, limiting their applications for quantum sensing. To address this issue, we develop an anti‐parity‐time‐symmetric model based on indirectly coupled waveguides and introduce a cascaded‐waveguide configuration that produces an effective rotation of the system's eigenbasis. This modification shifts the two‐photon bunching‐antibunching transition to coincide with the EP. Near the EP, a small refractive‐index perturbation leads to a sharp change in visibility, which becomes more pronounced by increasing waveguide length. This passive, gain‐free design may minimize noise and offer a feasible route toward EP‐enhanced quantum phase sensing on integrated platforms.
Exceptional points, where two or more eigenstates of a non-Hermitian system coalesce, are now of interest across many fields of physics, from the perspective of open-system dynamics, sensing, nonreciprocal transport, and topological phase transitions. In this work, we investigate exceptional points in cavity optomechanics, a platform of interest to diverse communities working on gravitational-wave detection, macroscopic quantum mechanics, quantum transduction, etc. Specifically, we clarify the role of quantum jumps in making a clear distinction between Liouvillian and Hamiltonian exceptional points in optomechanical systems. While the Liouvillian exceptional point arises from the unconditional Lindblad dynamics and is independent of the phonon-bath temperature, the Hamiltonian exceptional point emerges from the conditional no-jump evolution and acquires a thermal shift due to an enhanced conditional damping. Employing the thermofield formalism, we derive a unified spectral framework that interpolates between these regimes via an analytical hybrid-Liouvillian description. Remarkably, in the weak-quantum-jump regime, the exceptional point is perturbed only at the second order, highlighting the robustness of the Hamiltonian exceptional point under small hybrid perturbations. Our work reveals a continuous family of hybrid exceptional points, clarifies the operational and physical differences between the conditional and unconditional dissipative dynamics in optomechanical systems, and provides a probe for thermal baths.