Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2603.10654

Graph Symmetry Organizes Exceptional Dynamics in Open Quantum Systems

Eric R. Bittner, Bhavay Tyagi, Kevin E. Bassler

quant-phmath-phnlin.SISubmitted Mar 11, 2026• Announced Mar 12, 2026
arXivHTMLPDF

Abstract

Exceptional points (EPs), indicative of parity-time (PT) symmetry breaking, play a central role in non-Hermitian physics, yet most studies begin from deliberately engineered effective Hamiltonians whose parameters are tuned to exhibit exceptional behavior. In realistic open quantum systems, however, dynamics are governed by Lindblad superoperators whose spectral structure is high-dimensional, symmetry-constrained, and not obviously reducible to minimal non-Hermitian models. A general framework for discovering exceptional dynamics directly from microscopic dissipative models has been lacking. Here we introduce a symmetry-resolved approach for identifying and characterizing exceptional points directly from the full Liouvillian generator. Correlated dissipation induces graph symmetries that decompose Liouville space into low-dimensional invariant sectors, within which minimal non-Hermitian blocks govern the onset of EPs and PT-breaking behavior. We further introduce a numerical diagnostic - the exceptional-point strength $\mathcal{E}$ - based on eigenvector conditioning, which quantifies proximity to defective dynamics without requiring analytic reduction. Applied to tight-binding models with correlated dephasing and relaxation, the method reproduces analytically predicted exceptional seams and reveals universal scaling of $\mathcal{E}$ near EP manifolds. More broadly, the framework enables systematic discovery of hidden exceptional structure in complex or high-dimensional open systems and is naturally compatible with matrix-free and tensor-network implementations for scalable many-body applications.

Related papers

Liouvillian exceptional points of any order in dissipative linear bosonic systems: Coherence functions and switching between PT and anti- PT symmetries

Ievgen I. Arkhipov, Adam Miranowicz, Fabrizio Minganti +1 more

Usually, when investigating exceptional points (EPs) of an open Markovian bosonic system, one deals with spectral degeneracies of a non-Hermitian Hamiltonian (NHH), which can correctly describe the system dynamics only in the semiclassical regime. A recently proposed quantum Liouvillian framework [Minganti et al., Phys. Rev. A 100, 062131 (2019)] enables the complete determination of the dynamical properties of such systems and their EPs (referred to as Liouvillian EPs, or LEPs) in the quantum regime by taking into account the effects of quantum jumps, which are ignored in the NHH formalism. Moreover, the symmetry and eigenfrequency spectrum of the NHH become a part of much larger Liouvillian eigenspace. As such, the EPs of an NHH form a subspace of the LEPs. Here we show that once an NHH of a dissipative linear bosonic system exhibits an EP of a certain finite order $n$, it immediately implies that the corresponding LEP can become of any higher order $m\ensuremath{\ge}n$ defined in the infinite Hilbert space. These higher-order LEPs can be identified by the coherence and spectral functions at the steady state. The coherence functions can offer a convenient tool to probe extreme system sensitivity to external perturbations in the vicinity of higher-order LEPs. As an example, we study a linear bosonic system of a bimodal cavity with incoherent mode coupling to reveal its higher-order LEPs; particularly, of second and third order via first- and second-order coherence functions, respectively. Accordingly, these LEPs can be additionally revealed by squared and cubic Lorentzian spectral lineshapes in the power and intensity-fluctuation spectra. Moreover, we demonstrate that these EPs can also be associated with spontaneous parity-time ($\mathcal{PT}$) and anti-$\mathcal{PT}$-symmetry breaking in the system studied. These symmetries can be switched in the output fields (the so-called supermodes) of an additional linear coupler with a properly chosen coupling strength. Thus, we show that the initial loss-loss dynamics for the supermodes can be equivalent to the balanced gain-loss evolution.

arXiv:2006.03557•Physical Review A•Sep 11, 2020•73 citations

Multiblock exceptional points in open quantum systems

Aysel Shiralieva, Grigory A. Starkov, Björn Trauzettel

Open quantum systems can be approximately described by non-Hermitian Hamiltonians (NHHs) and Liouvillian superoperators. The two approaches differ by quantum jump terms corresponding to a measurement of the system by its environment. We analyze the emergence of exceptional points (EPs) in NHHs and Liouvillian superoperators. In particular, we show how EPs in NHHs relate to a novel type of EPs -- multi-block EPs -- in the no-jump Liouvillian, i.e. the Liouvillian superoperator in absence of quantum jump terms. We further analyze how quantum jump terms modify the multi-block structure. To illustrate our general findings, we present two prime examples: qubits and qutrits coupled to additional ground state levels that serve as sinks of the population. In those examples, we can navigate through the EP block structure by a variation of physical parameters. We analyze how the dynamics of the population of the states is affected by the order of the EPs. Additionally, we demonstrate that the quantum geometric tensor serves as a sensitive indicator of EPs of different kinds.

arXiv:2509.11856•Physical Review A•Mar 16, 2026•1 citation

Exceptional Points in Photonics: From Non-Hermitian Physics to Applications

Fan Zhang, Nikolay Solodovchenko, Dmitrii N. Maksimov +5 more

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.

physics.opticsCross-listedarXiv:2609.01239•Sep 2, 2026

Characterizing Liouvillian exceptional points through Newton polygons and tropical geometry

P Sayooj, Awadhesh Narayan

Abstract The dynamics of open quantum systems described by the Lindblad master equation follows according to non-Hermitian operators. As a result, such systems can host non-Hermitian degeneracies called Liouvillian exceptional points (EPs). In this work, we show that Newton polygons and tropical geometric approach allow identification and characterization of Liouvillian EPs. We use two models—dissipative spin − 1 / 2 system and dissipative superconducting qubit system—to illustrate our method. We demonstrate that our approach captures the anisotropy and order of the Liouvillian EPs, while also revealing the subtle dependence on the form of the perturbation. Our analytical analysis is supplemented by direct numerical calculations of the scaling and exchange of eigenvalues around Liouvillian EPs. Our analytical approach could be useful in understanding and designing Liouvillian EPs of desired order.

arXiv:2510.08156•Journal of Physics A Mathematical and Theoretical•Mar 20, 2026•0 citations

From Spectral Singularities to Multipartite Entanglement Scaling at Higher-Order Exceptional Points

Chunlai Yang, Shuheng Liu, Xinyao Huang +2 more

Exceptional points (EPs) are non-Hermitian spectral singularities exhibiting fractional-power responses, yet their implications for multipartite entanglement of interacting quantum many-body systems remain largely unexplored. Here we develop a general framework that links higher-order non-Hermitian degeneracies to the scaling behavior of genuine multipartite entanglement in interacting identical-qubit systems. Permutation symmetry of the identical qubits decomposes the exponentially large Hilbert space into independent irreducible-representation sectors, thereby constraining the maximal EP order of $N$ qubits to $N+1$ rather than $2^N$. Near an $n$th-order EP, genuine multipartite entanglement inherits the spectral response and generically exhibits a fractional-power scaling under weak perturbations. Explicit examples show that conventional two-body interactions support third- and fourth-order EPs with the corresponding entanglement responses, whereas higher-order EPs with genuine multipartite-entangled coalesced states require additional independent interaction channels, such as three-body interactions. Our results establish a fundamental connection among non-Hermitian degeneracies, multipartite entanglement, and symmetry, extending higher-order EP physics from spectral singularities to genuine many-body quantum correlations.

quant-pharXiv:2606.24205•Jun 24, 2026•0 citations

Experimental Determination of P T -Symmetric Exceptional Points in a Single Trapped Ion

Liangyu Ding, Kaiye Shi, Qiuxin Zhang +3 more

Exceptional points (EPs) of a non-Hermitian Hamiltonian with parity-time-reversal (PT) symmetry have the potential to drastically enhance the capabilities of metrology and sensing through their power-law growing sensitivity to external perturbation. With the ability of generating and tuning dissipation in a single trapped ion system, we observe rich dynamics and detailed quantum phase transitions from the PT-symmetric phase to the symmetry-breaking phase. In this single qubit full quantum system, we develop a method to precisely determine the location of EP without any fitting parameter, and extract the eigenvalues in a unified way through all parameter regions. We can also obtain the full density matrix by quantum state tomography. Finally, we suggest from theoretical analysis that the periodically driving PT-symmetric non-Hermitian system can be used to measure the magnitude, frequency, and phase of time-dependent perturbation with EP enhancement.

Physical Review Letters•Feb 23, 2021•159 citations
Exceptional points (EPs), indicative of parity-time (PT) symmetry breaking, play a central role in non-Hermitian physics, yet most studies begin from deliberately engineered effective Hamiltonians whose parameters are tuned to exhibit exceptional behavior. In realistic open quantum systems, however, dynamics are governed by Lindblad superoperators whose spectral structure is high-dimensional, symmetry-constrained, and not obviously reducible to minimal non-Hermitian models. A general framework for discovering exceptional dynamics directly from microscopic dissipative models has been lacking. Here we introduce a symmetry-resolved approach for identifying and characterizing exceptional points directly from the full Liouvillian generator. Correlated dissipation induces graph symmetries that decompose Liouville space into low-dimensional invariant sectors, within which minimal non-Hermitian blocks govern the onset of EPs and PT-breaking behavior. We further introduce a numerical diagnostic - the exceptional-point strength E\mathcal{E}E - based on eigenvector conditioning, which quantifies proximity to defective dynamics without requiring analytic reduction. Applied to tight-binding models with correlated dephasing and relaxation, the method reproduces analytically predicted exceptional seams and reveals universal scaling of E\mathcal{E}E near EP manifolds. More broadly, the framework enables systematic discovery of hidden exceptional structure in complex or high-dimensional open systems and is naturally compatible with matrix-free and tensor-network implementations for scalable many-body applications.
Usually, when investigating exceptional points (EPs) of an open Markovian bosonic system, one deals with spectral degeneracies of a non-Hermitian Hamiltonian (NHH), which can correctly describe the system dynamics only in the semiclassical regime. A recently proposed quantum Liouvillian framework [Minganti et al., Phys. Rev. A 100, 062131 (2019)] enables the complete determination of the dynamical properties of such systems and their EPs (referred to as Liouvillian EPs, or LEPs) in the quantum regime by taking into account the effects of quantum jumps, which are ignored in the NHH formalism. Moreover, the symmetry and eigenfrequency spectrum of the NHH become a part of much larger Liouvillian eigenspace. As such, the EPs of an NHH form a subspace of the LEPs. Here we show that once an NHH of a dissipative linear bosonic system exhibits an EP of a certain finite order nnn, it immediately implies that the corresponding LEP can become of any higher order $m\ensuremath{\ge}n$ defined in the infinite Hilbert space. These higher-order LEPs can be identified by the coherence and spectral functions at the steady state. The coherence functions can offer a convenient tool to probe extreme system sensitivity to external perturbations in the vicinity of higher-order LEPs. As an example, we study a linear bosonic system of a bimodal cavity with incoherent mode coupling to reveal its higher-order LEPs; particularly, of second and third order via first- and second-order coherence functions, respectively. Accordingly, these LEPs can be additionally revealed by squared and cubic Lorentzian spectral lineshapes in the power and intensity-fluctuation spectra. Moreover, we demonstrate that these EPs can also be associated with spontaneous parity-time (PT\mathcal{PT}PT) and anti-PT\mathcal{PT}PT-symmetry breaking in the system studied. These symmetries can be switched in the output fields (the so-called supermodes) of an additional linear coupler with a properly chosen coupling strength. Thus, we show that the initial loss-loss dynamics for the supermodes can be equivalent to the balanced gain-loss evolution.
Open quantum systems can be approximately described by non-Hermitian Hamiltonians (NHHs) and Liouvillian superoperators. The two approaches differ by quantum jump terms corresponding to a measurement of the system by its environment. We analyze the emergence of exceptional points (EPs) in NHHs and Liouvillian superoperators. In particular, we show how EPs in NHHs relate to a novel type of EPs -- multi-block EPs -- in the no-jump Liouvillian, i.e. the Liouvillian superoperator in absence of quantum jump terms. We further analyze how quantum jump terms modify the multi-block structure. To illustrate our general findings, we present two prime examples: qubits and qutrits coupled to additional ground state levels that serve as sinks of the population. In those examples, we can navigate through the EP block structure by a variation of physical parameters. We analyze how the dynamics of the population of the states is affected by the order of the EPs. Additionally, we demonstrate that the quantum geometric tensor serves as a sensitive indicator of EPs of different kinds.
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.
Abstract The dynamics of open quantum systems described by the Lindblad master equation follows according to non-Hermitian operators. As a result, such systems can host non-Hermitian degeneracies called Liouvillian exceptional points (EPs). In this work, we show that Newton polygons and tropical geometric approach allow identification and characterization of Liouvillian EPs. We use two models—dissipative spin − 1 / 2 system and dissipative superconducting qubit system—to illustrate our method. We demonstrate that our approach captures the anisotropy and order of the Liouvillian EPs, while also revealing the subtle dependence on the form of the perturbation. Our analytical analysis is supplemented by direct numerical calculations of the scaling and exchange of eigenvalues around Liouvillian EPs. Our analytical approach could be useful in understanding and designing Liouvillian EPs of desired order.
Exceptional points (EPs) are non-Hermitian spectral singularities exhibiting fractional-power responses, yet their implications for multipartite entanglement of interacting quantum many-body systems remain largely unexplored. Here we develop a general framework that links higher-order non-Hermitian degeneracies to the scaling behavior of genuine multipartite entanglement in interacting identical-qubit systems. Permutation symmetry of the identical qubits decomposes the exponentially large Hilbert space into independent irreducible-representation sectors, thereby constraining the maximal EP order of NNN qubits to N+1N+1N+1 rather than 2N2^N2N. Near an nnnth-order EP, genuine multipartite entanglement inherits the spectral response and generically exhibits a fractional-power scaling under weak perturbations. Explicit examples show that conventional two-body interactions support third- and fourth-order EPs with the corresponding entanglement responses, whereas higher-order EPs with genuine multipartite-entangled coalesced states require additional independent interaction channels, such as three-body interactions. Our results establish a fundamental connection among non-Hermitian degeneracies, multipartite entanglement, and symmetry, extending higher-order EP physics from spectral singularities to genuine many-body quantum correlations.
Exceptional points (EPs) of a non-Hermitian Hamiltonian with parity-time-reversal (PT) symmetry have the potential to drastically enhance the capabilities of metrology and sensing through their power-law growing sensitivity to external perturbation. With the ability of generating and tuning dissipation in a single trapped ion system, we observe rich dynamics and detailed quantum phase transitions from the PT-symmetric phase to the symmetry-breaking phase. In this single qubit full quantum system, we develop a method to precisely determine the location of EP without any fitting parameter, and extract the eigenvalues in a unified way through all parameter regions. We can also obtain the full density matrix by quantum state tomography. Finally, we suggest from theoretical analysis that the periodically driving PT-symmetric non-Hermitian system can be used to measure the magnitude, frequency, and phase of time-dependent perturbation with EP enhancement.