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:2411.14599 · Physical Review A

Limits of the non-Hermitian description of decay models

Kyle Monkman, Mona Berciu

Published Feb 19, 2026• 2 citations
arXivHTMLPDF

Abstract

We present a general proof that non-Hermitian dynamics and Lindblad dynamics with only decay terms are equivalent in the highest particle subspace. We then propose an unbiased method to determine if a system's dynamics in the highest-particle subspace is non-Hermitian. We exemplify this for a simple two-site decay system connected to two baths, and find that the exact solution is well approximated by non-Hermitian dynamics only in the weak-coupling and in the singular-coupling limits, where a Lindbladian description was already known to be accurate. The fact that an accurate non-Hermitian description is so limited, even for such a simple system, raises doubts about how valid such descriptions are for more complicated systems away from these asymptotic limits. Finally, we prove that for models with a nondegenerate system Hamiltonian, exceptional points cannot occur in the weak-coupling limit. This result is relevant for the design of experiments that aim to identify such exceptional points.

DOI
10.1103/dyjw-1cbl

Related papers

Local and Global Master Equations through the Lens of Non-Hermitian Physics

Grazia Di Bello, Fabrizio Pavan, Vittorio Cataudella +1 more

We investigate the relation between non-Hermitian Hamiltonian and Lindblad dynamics in nonequilibrium open quantum systems. Non-Hermitian models can extend phase diagrams and enable sensing advantages, but such effects often rely on postselection, raising questions about their relevance for unconditional dynamics. Using a minimal two-qubit setup mediating a heat current, we compare local and global Markovian master equations with their non-Hermitian counterparts. We observe that exceptional points emerge only in the local master equation and in the corresponding non-Hermitian Hamiltonian at sufficiently strong nonequilibrium. We further consider hybrid configurations, where one bath is treated with a Lindblad description and the other with a non-Hermitian approach, interpolating between the two extremes. Our results contribute understanding the role of quantum jumps and exceptional points in nonequilibrium open quantum systems and identify a simple, experimentally accessible architecture, realizable, for instance, in circuit-QED platforms, for their exploration.

quant-pharXiv:2603.23011•Mar 25, 2026•1 citation

Quasi-Hermitian proxy for the conditional no-jump dynamics in a three-site model

Aritra Ghosh, Miloslav Znojil

Abstract In this work, we show that in the regime of real and non-degenerate spectrum, the quasi-Hermitian framework provides an effective description of the conditional no-jump evolution of certain Markovian open systems within invariant subspaces while the full Lindblad dynamics governs the unconditional dynamics which includes quantum jumps. We present a three-site fermionic model with asymmetric hopping amplitudes whose single-particle generator is intrinsically non-Hermitian yet supports an all-real spectrum in a finite region of the parameter space. We construct an explicit Lindbladian-based embedding in which the same Hamiltonian arises as the no-jump generator of a completely positive and trace-preserving Lindblad equation, up to a particle-decay term. Due to particle-number conservation, this shift reduces to a scalar within each fixed-particle-number sector. We further analyze the single-particle spectrum and identify a third-order exceptional point that lies on the boundary marking the breakdown of quasi-hermiticity in a given fixed-particle-number sector.

Europhysics Letters (EPL)•Mar 1, 2026•0 citations

A continuous transformation between non-Hermitian Hamiltonian and Lindbladian evolution

Daniel Finkelstein‐Shapiro

Non-Hermitian Hamiltonians and Lindblad operators are some of the most important generators of dynamics for describing quantum systems interacting with different kinds of environments. The first type differs from conservative evolution by an anti-Hermitian term that causes particle decay, while the second type differs by a dissipation operator in Lindblad form that allows energy exchange with a bath. However, although under some conditions the two types of maps can be used to describe the same observable, they form a disjoint set. In this work, we propose a generalized generator of dynamics of the form $L_\text{mixed}(z,ρ_S) = -i[H,ρ_S] + \sum_i \left(\frac{Γ_{c,i}}{z+Γ_{c,i}}F_iρ_S F_i^{\dagger} -\frac{1}{2} \{F_i^{\dagger} F_i,ρ_S \}_+\right)$ that depends on a general energy $z$, and has a tunable parameter $Γ_c$ that determines the degree of particle density lost. It has as its limits non-Hermitian ($Γ_c \to 0$) and Lindbladian dynamics ($Γ_c \to \infty$). The intermediate regime evolves density matrices such that $0 \leq \text{Tr} (ρ_S) \leq 1$. We derive our generator with the help of an ancillary continuum manifold acting as a sink for particle density. The evolution describes a system that can exchange both particle density and energy with its environment. We illustrate its features for a two level system and a five $M$ level system with a coherent population trapping point.

arXiv:2208.03310•Aug 5, 2022•0 citations

Non-Hermitian Degeneracies in unitary quantum dynamics interrupted by repetitive quantum measurements

S. Kar, Supervisor Dr. Sourin Das

The effect of repeated measurements on unitary evolution of a quantum system at regular intervals has been studied picking a specific example of a quantum, particle moving on a lattice of three sites. Dividing the system into two subsystems, we obtain the survival probability of the particle (i.e. particle not being detected) by time evolution followed by projection onto one subsystem. Using this evolution operator we obtain the expression for effective non-Hermitian Hamiltonian whose dynamics could be mapped to a general firs-order perturbation approach. We obtained a good argument between three approaches followed for calculating the survival probability, namely, the first order perturbative approach, the exact non-hermitian evolution and repeated the non-hermitian measurements interrupting the unitary evolution. Further we obtained the non-Hermitian degeneracies called Exceptional Points using the effective Hamiltonian. Finally, the presence of exceptional point is verified by decomposing the initial state into eigenstates of effective Hamiltonian and observing the behavior of the coefficients of decomposition while traversing through each parameter on which the exceptional point depends.

•Apr 1, 2018•0 citations

Non-Markovian quantum exceptional points

Jhen-Dong Lin, Po-Chen Kuo, Neill Lambert +3 more

Exceptional points (EPs) are singularities in the spectra of non-Hermitian operators where eigenvalues and eigenvectors coalesce. Open quantum systems have recently been explored as EP testbeds due to their non-Hermitian nature. However, most studies focus on the Markovian limit, leaving a gap in understanding EPs in the non-Markovian regime. This work addresses this gap by proposing a general framework based on two numerically exact descriptions of non-Markovian dynamics: the pseudomode equation of motion (PMEOM) and the hierarchical equations of motion (HEOM). The PMEOM is particularly useful due to its Lindblad-type structure, aligning with previous studies in the Markovian regime while offering deeper insights into EP identification. This framework incorporates non-Markovian effects through auxiliary degrees of freedom, enabling the discovery of additional or higher-order EPs that are inaccessible in the Markovian regime. We demonstrate the utility of this approach using the spin-boson model and linear bosonic systems. The full description of exceptional points in the non-Markovian regime is complicated by the unclear applicability of standard techniques such as spectral analysis. Here, the authors fill this gap by proposing a general framework that combines the pseudomode equation of motion and the hierarchical equations of motion.

arXiv:2406.18362•Nature Communications•Feb 3, 2025•38 citations

Multiple quantum exceptional, diabolical, and hybrid points in multimode bosonic systems: II. Nonconventional PT-symmetric dynamics and unidirectional coupling

Jan Peřina, Kishore Thapliyal, Grzegorz Chimczak +2 more

We analyze the existence and degeneracies of quantum exceptional, diabolical, and hybrid points in simple bosonic systems - comprising up to six modes with damping and/or amplification - under two complementary scenarios to those of Ref. \cite{Thapliyal2025}: (i) nonconventional PT-symmetric dynamics confined to a subspace of the full Liouville space, and (ii) systems featuring unidirectional coupling. The system dynamics described by quadratic non-Hermitian Hamiltonians is governed by the Heisenberg-Langevin equations. Conditions for the observation of inherited quantum hybrid points with up to sixth-order exceptional and second-order diabolical degeneracies are revealed, though relevant only for short-time dynamics. This raises the question of whether higher-order inherited singularities exist in bosonic systems under general conditions. Nevertheless, for short times, unidirectional coupling of various types enables the concatenation of simple bosonic systems with second- and third-order exceptional degeneracies such that arbitrarily high exceptional degeneracies are reached. Methods for numerical identifying the quantum exceptional and hybrid points together with their degeneracies are addressed. Following Ref. \cite{Thapliyal2025} rich dynamics of second-order field-operator moments is analyzed from the point of view of the presence of exceptional and diabolical points and their degeneracies.

arXiv:2405.01667•Quantum•Dec 10, 2025•3 citations
We present a general proof that non-Hermitian dynamics and Lindblad dynamics with only decay terms are equivalent in the highest particle subspace. We then propose an unbiased method to determine if a system's dynamics in the highest-particle subspace is non-Hermitian. We exemplify this for a simple two-site decay system connected to two baths, and find that the exact solution is well approximated by non-Hermitian dynamics only in the weak-coupling and in the singular-coupling limits, where a Lindbladian description was already known to be accurate. The fact that an accurate non-Hermitian description is so limited, even for such a simple system, raises doubts about how valid such descriptions are for more complicated systems away from these asymptotic limits. Finally, we prove that for models with a nondegenerate system Hamiltonian, exceptional points cannot occur in the weak-coupling limit. This result is relevant for the design of experiments that aim to identify such exceptional points.
We investigate the relation between non-Hermitian Hamiltonian and Lindblad dynamics in nonequilibrium open quantum systems. Non-Hermitian models can extend phase diagrams and enable sensing advantages, but such effects often rely on postselection, raising questions about their relevance for unconditional dynamics. Using a minimal two-qubit setup mediating a heat current, we compare local and global Markovian master equations with their non-Hermitian counterparts. We observe that exceptional points emerge only in the local master equation and in the corresponding non-Hermitian Hamiltonian at sufficiently strong nonequilibrium. We further consider hybrid configurations, where one bath is treated with a Lindblad description and the other with a non-Hermitian approach, interpolating between the two extremes. Our results contribute understanding the role of quantum jumps and exceptional points in nonequilibrium open quantum systems and identify a simple, experimentally accessible architecture, realizable, for instance, in circuit-QED platforms, for their exploration.
Abstract In this work, we show that in the regime of real and non-degenerate spectrum, the quasi-Hermitian framework provides an effective description of the conditional no-jump evolution of certain Markovian open systems within invariant subspaces while the full Lindblad dynamics governs the unconditional dynamics which includes quantum jumps. We present a three-site fermionic model with asymmetric hopping amplitudes whose single-particle generator is intrinsically non-Hermitian yet supports an all-real spectrum in a finite region of the parameter space. We construct an explicit Lindbladian-based embedding in which the same Hamiltonian arises as the no-jump generator of a completely positive and trace-preserving Lindblad equation, up to a particle-decay term. Due to particle-number conservation, this shift reduces to a scalar within each fixed-particle-number sector. We further analyze the single-particle spectrum and identify a third-order exceptional point that lies on the boundary marking the breakdown of quasi-hermiticity in a given fixed-particle-number sector.
Non-Hermitian Hamiltonians and Lindblad operators are some of the most important generators of dynamics for describing quantum systems interacting with different kinds of environments. The first type differs from conservative evolution by an anti-Hermitian term that causes particle decay, while the second type differs by a dissipation operator in Lindblad form that allows energy exchange with a bath. However, although under some conditions the two types of maps can be used to describe the same observable, they form a disjoint set. In this work, we propose a generalized generator of dynamics of the form Lmixed(z,ρS)=−i[H,ρS]+∑i(Γc,iz+Γc,iFiρSFi†−12{Fi†Fi,ρS}+)L_\text{mixed}(z,ρ_S) = -i[H,ρ_S] + \sum_i \left(\frac{Γ_{c,i}}{z+Γ_{c,i}}F_iρ_S F_i^{\dagger} -\frac{1}{2} \{F_i^{\dagger} F_i,ρ_S \}_+\right)Lmixed​(z,ρS​)=−i[H,ρS​]+∑i​(z+Γc,i​Γc,i​​Fi​ρS​Fi†​−21​{Fi†​Fi​,ρS​}+​) that depends on a general energy zzz, and has a tunable parameter ΓcΓ_cΓc​ that determines the degree of particle density lost. It has as its limits non-Hermitian (Γc→0Γ_c \to 0Γc​→0) and Lindbladian dynamics (Γc→∞Γ_c \to \inftyΓc​→∞). The intermediate regime evolves density matrices such that 0≤Tr(ρS)≤10 \leq \text{Tr} (ρ_S) \leq 10≤Tr(ρS​)≤1. We derive our generator with the help of an ancillary continuum manifold acting as a sink for particle density. The evolution describes a system that can exchange both particle density and energy with its environment. We illustrate its features for a two level system and a five MMM level system with a coherent population trapping point.
The effect of repeated measurements on unitary evolution of a quantum system at regular intervals has been studied picking a specific example of a quantum, particle moving on a lattice of three sites. Dividing the system into two subsystems, we obtain the survival probability of the particle (i.e. particle not being detected) by time evolution followed by projection onto one subsystem. Using this evolution operator we obtain the expression for effective non-Hermitian Hamiltonian whose dynamics could be mapped to a general firs-order perturbation approach. We obtained a good argument between three approaches followed for calculating the survival probability, namely, the first order perturbative approach, the exact non-hermitian evolution and repeated the non-hermitian measurements interrupting the unitary evolution. Further we obtained the non-Hermitian degeneracies called Exceptional Points using the effective Hamiltonian. Finally, the presence of exceptional point is verified by decomposing the initial state into eigenstates of effective Hamiltonian and observing the behavior of the coefficients of decomposition while traversing through each parameter on which the exceptional point depends.
Exceptional points (EPs) are singularities in the spectra of non-Hermitian operators where eigenvalues and eigenvectors coalesce. Open quantum systems have recently been explored as EP testbeds due to their non-Hermitian nature. However, most studies focus on the Markovian limit, leaving a gap in understanding EPs in the non-Markovian regime. This work addresses this gap by proposing a general framework based on two numerically exact descriptions of non-Markovian dynamics: the pseudomode equation of motion (PMEOM) and the hierarchical equations of motion (HEOM). The PMEOM is particularly useful due to its Lindblad-type structure, aligning with previous studies in the Markovian regime while offering deeper insights into EP identification. This framework incorporates non-Markovian effects through auxiliary degrees of freedom, enabling the discovery of additional or higher-order EPs that are inaccessible in the Markovian regime. We demonstrate the utility of this approach using the spin-boson model and linear bosonic systems. The full description of exceptional points in the non-Markovian regime is complicated by the unclear applicability of standard techniques such as spectral analysis. Here, the authors fill this gap by proposing a general framework that combines the pseudomode equation of motion and the hierarchical equations of motion.
We analyze the existence and degeneracies of quantum exceptional, diabolical, and hybrid points in simple bosonic systems - comprising up to six modes with damping and/or amplification - under two complementary scenarios to those of Ref. \cite{Thapliyal2025}: (i) nonconventional PT-symmetric dynamics confined to a subspace of the full Liouville space, and (ii) systems featuring unidirectional coupling. The system dynamics described by quadratic non-Hermitian Hamiltonians is governed by the Heisenberg-Langevin equations. Conditions for the observation of inherited quantum hybrid points with up to sixth-order exceptional and second-order diabolical degeneracies are revealed, though relevant only for short-time dynamics. This raises the question of whether higher-order inherited singularities exist in bosonic systems under general conditions. Nevertheless, for short times, unidirectional coupling of various types enables the concatenation of simple bosonic systems with second- and third-order exceptional degeneracies such that arbitrarily high exceptional degeneracies are reached. Methods for numerical identifying the quantum exceptional and hybrid points together with their degeneracies are addressed. Following Ref. \cite{Thapliyal2025} rich dynamics of second-order field-operator moments is analyzed from the point of view of the presence of exceptional and diabolical points and their degeneracies.