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.
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.
In recent years, significant progress has been made in utilizing the divergence of spectrum response rate at the exceptional point (EP) for sensing in classical systems, while the use and characterization of quantum EPs for sensing have been largely unexplored. For a quantum EP sensor, an important issue is the relation between the order of the quantum EP and the scaling of quantum Fisher information (QFI), an essential quantity for characterizing quantum sensors. Here we investigate multi-mode quadratic bosonic systems, which exhibit higher-order EP dynamics, but possess Hermitian Hamiltonians without Langevin noise, thus can be utilized for quantum sensing. We derive an exact analytic formula for the QFI, from which we establish a scaling relation between the QFI and the order of the EP. We apply the formula to study a three-mode EP sensor and a multi-mode bosonic Kitaev chain and show that the EP physics can significantly enhance the sensing sensitivity. Our work establishes the connection between two important fields: non-Hermitian EP dynamics and quantum sensing, and may find important applications in quantum information and quantum non-Hermitian physics.
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.
Open photonic systems provide a versatile platform for non-Hermitian physics, enabling control over complex spectra, transport, and light-matter interactions. Exceptional points (EPs), at which eigenvalues and eigenvectors coalesce and the governing operator becomes defective, play a central role because they combine branch-point spectral topology, nonanalytic perturbative response, and controllable eigenstate conversion. This Review provides a unified framework for EP photonics by systematically distinguishing exceptional degeneracies according to the underlying operator, spectral variable, boundary conditions, and experimentally accessible observables. We discuss Hamiltonian EPs, absorbing EPs associated with scattering zeros, real-frequency scattering-matrix and Jones-matrix EPs, Bloch and Floquet EPs, and Liouvillian EPs in open quantum systems. We review their spectral topology, static and dynamical encircling, higher-order exceptional structures, and coexistence with bound states in the continuum, together with applications in sensing, lasing, coherent absorption, directional scattering, polarization and wavefront control, nonlinear optics, optical storage, nonreciprocal photonics, and quantum photonics. We also critically assess the current limitations, practical challenges, and future perspectives of EP-based photonic technologies, with particular attention to robustness, noise, scalability, and experimentally measurable performance.
There has been debate around applicability of exceptional points (EPs) for quantum sensing. To resolve this, we first explore how to experimentally implement the non-Hermitian non-diagonalizable Hamiltonians, which exhibit EPs, in quantum computers that run on unitary gates. We propose to use an ancilla-based method in this regard. Next, we show how such Hamiltonians can be used for parameter estimation using quantum computers and analyze its performance in terms of the quantum Fisher information (QFI) at EPs, both without noise and in the presence of noise. It is well known that QFI of a parameter to be estimated is inversely related to the variance of the parameter by the quantum Cramer–Rao bound. Therefore, the divergence of the QFI at EPs promises sensing advantages. We experimentally demonstrate in a cloud quantum architecture and theoretically show, using Puiseux series, that the QFI indeed diverges in such EP systems that were earlier considered to be non-divergent.
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.
Abstract The exceptional points (EPs) of non-Hermitian systems, where n different energy eigenstates merge into an identical one, have many intriguing properties that have no counterparts in Hermitian systems. In particular, the ϵ 1 / n dependence of the energy level splitting on a perturbative parameter ϵ near an n th order EP stimulates the idea of metrology with arbitrarily high sensitivity, since the susceptibility d ϵ 1/ n /d ϵ diverges at the EP. Here we theoretically study the sensitivity of parameter estimation near the EPs, using the exact formalism of quantum Fisher information (QFI). The QFI formalism allows the highest sensitivity to be determined without specifying a specific measurement approach. We find that the EP bears no dramatic enhancement of the sensitivity. Instead, the coalescence of the eigenstates exactly counteracts the eigenvalue susceptibility divergence and makes the sensitivity a smooth function of the perturbative parameter.