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Steady-State Noise Signatures of Lindbladian Exceptional Points

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Pith's one-line read Current noise in steady state reveals signatures of Lindbladian exceptional points through time-delayed correlations.

desk verdict The paper derives steady-state current correlations to detect Lindbladian EPs and illustrates the idea on two qubits, but the expressions may not properly handle the non-diagonalizable case at the EP itself. read the letter →

arxiv 2606.13377 v1 pith:EGOSIPKY submitted 2026-06-11 quant-ph cond-mat.mes-hall

Shihang Pan (1) , Gianmichele Blasi (1 , 2) , Géraldine Haack (1) ((1) Department of Applied Physics , University of Geneva , Geneva , Switzerland , (2) Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB)
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Palma de Mallorca Spain)
This is my paper · ORCID
classification quant-phcond-mat.mes-hall
keywords Lindbladianexceptionalpointscurrentnoisesteady-statecorrelationsopenquantumsystemstime-delaydependencetwo-qubitmodeldissipativedynamics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper shows that while average steady-state currents give no direct sign of exceptional points in the Lindbladian, the current correlation functions do. It derives general expressions for these correlations inside the Lindblad master-equation framework and demonstrates that the points alter how the correlations depend on time delay. In the concrete case of two interacting qubits coupled to two reservoirs, the noise separates overdamped, underdamped, and critical regimes. This turns steady-state noise into a practical probe for non-Hermitian degeneracies in open quantum systems.

What carries the argument

General expressions for current correlation functions obtained from the Lindblad master equation, which carry the effect of eigenvalue and eigenvector coalescence at the exceptional point into the steady-state noise as a function of time delay.

What would settle it

Measure current correlation functions versus time delay in a two-qubit system tuned across an exceptional point and check whether the predicted separation into overdamped, underdamped, and critical regimes appears.

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Extended reading notes

Core claim

Signatures of Lindbladian exceptional points, previously seen only in transient observables, appear in steady-state current correlation functions; the functions' time-delay dependence encodes the coalescence of eigenvalues and eigenvectors, as derived from the Lindblad master equation and illustrated by the two-qubit example that distinguishes the three dynamical regimes.

Load-bearing premise

The general expressions for current correlation functions derived from the Lindblad master equation correctly encode the coalescence of eigenvalues and eigenvectors at the exceptional point.

Editorial extensions

If this is right

  • Current correlation functions distinguish overdamped, underdamped, and critical regimes even when average currents remain featureless.
  • Steady-state noise supplies direct evidence of the exceptional-point structure in the Lindbladian.
  • The time-delay dependence of the correlations is modified by the coalescence at the exceptional point.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Noise measurements could locate Lindbladian exceptional points in a wider range of open systems without needing time-resolved transients.
  • The same correlation-function approach may apply to other steady-state observables governed by Lindblad dynamics.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that Lindbladian exceptional points, while invisible in steady-state average currents, produce detectable signatures in steady-state current noise. It derives general expressions for two-time current correlation functions C(τ) within the Lindblad master-equation framework and shows that these functions encode the coalescence of eigenvalues and eigenvectors at the EP through their time-delay dependence. The results are illustrated with a two-qubit system coupled to two reservoirs, where the noise distinguishes overdamped, underdamped, and critical regimes.

Significance. If the derivations hold, the work supplies a concrete steady-state observable for Lindbladian EPs that complements transient probes. The general expressions for current correlators, if they correctly treat the non-diagonalizable case, would constitute a useful technical advance for open quantum systems and quantum transport.

major comments (2)
  1. [General expressions for current correlation functions] The derivation of the current correlation functions (general expressions section) relies on the propagator e^{ℒ τ} or equivalent spectral decomposition of the Liouvillian. At an EP the Liouvillian is non-diagonalizable and the standard decomposition L = Σ λ_k |r_k⟩⟨l_k| is invalid; the correct form requires polynomial prefactors (τ e^{λ τ}) arising from the Jordan block. The manuscript must explicitly state whether the general expressions or the two-qubit calculation incorporate these terms; otherwise the claimed distinction between regimes at the critical point does not follow.
  2. [Two-qubit example] Two-qubit illustration: the text describes the model and states that steady-state noise distinguishes the three regimes, but the explicit functional forms or numerical plots of C(τ) at, above, and below the EP are not provided. Without these data the claim that the noise signatures are generic and observable remains unverified.
minor comments (2)
  1. [Notation] Notation for the current operator and the precise definition of the steady-state average ⟨…⟩_ss should be stated once at the beginning of the derivation section for clarity.
  2. [Abstract] The abstract refers to 'current noise' without specifying whether it is the zero-frequency noise or the full frequency-dependent spectrum; the manuscript should align terminology between abstract and main text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and insightful comments, which help clarify the technical presentation of our results on current noise at Lindbladian exceptional points. We address each major comment below.

read point-by-point responses

  1. Referee: [General expressions for current correlation functions] The derivation of the current correlation functions (general expressions section) relies on the propagator e^{ℒ τ} or equivalent spectral decomposition of the Liouvillian. At an EP the Liouvillian is non-diagonalizable and the standard decomposition L = Σ λ_k |r_k⟩⟨l_k| is invalid; the correct form requires polynomial prefactors (τ e^{λ τ}) arising from the Jordan block. The manuscript must explicitly state whether the general expressions or the two-qubit calculation incorporate these terms; otherwise the claimed distinction between regimes at the critical point does not follow.

    Authors: Our general expressions for the two-time current correlators are written directly in terms of the time-ordered propagator e^{ℒ τ} (or its adjoint action on the current superoperators), which is mathematically well-defined for any finite-dimensional Liouvillian, including at exceptional points where ℒ is non-diagonalizable. The spectral decomposition into left and right eigenvectors is used only in the generic (diagonalizable) regime for interpretive purposes. In the two-qubit example the correlators are obtained by direct integration of the master equation, which automatically incorporates the correct Jordan-block structure. Nevertheless, we agree that an explicit statement is needed; in the revision we will add a dedicated paragraph deriving the polynomial prefactors for the non-diagonalizable case and confirming that the reported distinction between overdamped, underdamped and critical regimes survives this more general expansion. revision: yes

  2. Referee: [Two-qubit example] Two-qubit illustration: the text describes the model and states that steady-state noise distinguishes the three regimes, but the explicit functional forms or numerical plots of C(τ) at, above, and below the EP are not provided. Without these data the claim that the noise signatures are generic and observable remains unverified.

    Authors: We accept that the current manuscript would benefit from more explicit verification. In the revised version we will supply (i) closed-form expressions for C(τ) obtained by solving the 4×4 Liouvillian in each regime and (ii) numerical plots of the normalized correlator versus delay τ for representative parameter values above, at, and below the exceptional point. These additions will make the claimed distinction between the three dynamical regimes directly visible to the reader. revision: yes

Circularity Check

0 steps flagged · score 2.0 of 10

Derivation of current correlators grounded in Lindblad framework with no load-bearing self-citation or definitional reduction

full rationale

The paper derives general expressions for current correlation functions directly from the Lindblad master-equation framework and illustrates them with a two-qubit example. No quoted steps reduce a prediction to a fitted input, self-citation chain, or ansatz smuggled via prior work by the same authors. The skeptic concern about spectral decomposition at EPs is a potential correctness issue (Jordan-block handling) rather than a circularity reduction shown by the paper's own equations. This is the common honest non-finding for a self-contained derivation.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

The claim rests on the standard Lindblad master-equation framework (domain assumption) and the validity of the derived correlation-function expressions (unstated derivation steps). No free parameters or invented entities are mentioned in the abstract.

assumptions (1)
  • domain assumption The system dynamics are accurately captured by a Lindblad master equation with Markovian reservoirs.
    Invoked throughout the abstract as the governing framework for both the general expressions and the two-qubit example.

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Cite this review

Pith. "Pith review of Steady-State Noise Signatures of Lindbladian Exceptional Points." pith.science (2026). https://pith.science/paper/EGOSIPKY

@misc{pith2026260613377,
  author       = {Pith},
  title        = {Pith review of: Steady-State Noise Signatures of Lindbladian Exceptional Points},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EGOSIPKY}},
  note         = {Machine review of arXiv:2606.13377}
}
read the original abstract

Exceptional points (EPs) are non-Hermitian degeneracies at which two or more eigenvalues and their corresponding eigenvectors coalesce. In open quantum systems, exceptional points can arise in the Lindbladian governing the dissipative dynamics. Their signatures have so far been mainly identified in finite-time observables, such as transient currents, while steady-state average currents generally provide no direct evidence of the underlying exceptional-point structure. In this work, we demonstrate that signatures of Lindbladian EPs can nevertheless be accessed in the steady-state regime through current noise. We derive general expressions for current correlation functions within a Lindblad master-equation framework and show, in particular, how exceptional points affect their behaviour as a function of the time delay. We illustrate these results with the paradigmatic example of two interacting qubits coupled to two reservoirs, where the steady-state noise clearly distinguishes overdamped, underdamped, and critical regimes. Our results establish current correlation functions as a steady-state probe of Lindbladian EPs in open quantum systems.

Figures

Figures reproduced from arXiv: 2606.13377 by the authors.

Figure 1
Figure 1. Sketch of a two-qubit system with the following parameters, bare energy of the two qubits [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Spectrum of the reduced Lindbladian σ  L˜  on a complex plane showing the coalescence of λ4, λ5 and λ6 at a third-order exceptional point. Color blue represents overdamped regime where η is real while red meas underdamped regime and we change η to iη. Its dynamics is given by the Lindblad equation in Eq. (6) if γi ≪ ϵ, g ≪ ϵ and g ≲ γi to ensure its validity as discussed previously. For a two-qubit system, the dim… view at source ↗
Figure 3
Figure 3. Currents as a function of time. 3a and 3b show the dynamics of I1 (t) and I2 (t) respectively. Both are normalized by their steady-state values. The initial steady is a product of thermal state. We choose the following set of parameters ξ = {ϵ = 1, γ1 = 0.05, γ2 = 0.01, T1 = 1, T2 = 0.5}. And the coupling strength g in each regime are gη2>0 = ¯g/2 and gη2<0 = 5¯g, where ¯g = |γ1 − γ2| /4 = 0.01 represents the value … view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Steady-state noise as a function of the time delay [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: Shot noise as a function of g. Orange solid line and cyan solid represent shot noises of auto- and cross-correlation functions. Red dashed line corresponds to the critical line, which separates overdamped (light green area) and underdamped (light blue area) regimes. We…

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