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arxiv: 2605.01912 · v1 · submitted 2026-05-03 · 🪐 quant-ph · cond-mat.str-el

Quantum-enhanced sensing from the interplay of long-range interactions and non-Hermiticity

Keshav Das Agarwal , Tanoy Kanti Konar , Leela Ganesh Chandra Lakkaraju , Aditi Sen De This is my paper

Pith reviewed 2026-05-09 17:18 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.str-el
keywords quantum sensinglong-range interactionsnon-Hermitian systemsquantum Fisher informationspin modelsparameter estimationopen quantum systems
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The pith

Tuning long-range interactions in a non-Hermitian spin model improves the scaling of quantum Fisher information for estimating magnetic field and anisotropy.

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

The paper studies parameter estimation in a long-range XX spin chain coupled to a reservoir, which produces an effective non-Hermitian iXY model whose couplings decay algebraically over a tunable range. By tracking the dynamical quantum Fisher information from a fully polarized initial state, the authors show that both time and system-size scaling of this quantity can be made better in the long-range regime than in the short-range regime. The same non-Hermitian long-range dynamics can also outperform the corresponding Hermitian long-range model, pointing to a metrological gain that arises only when long-range couplings and non-Hermiticity act together. At the critical magnetic field, however, the scaling reverts to the same value for both Hermitian and non-Hermitian versions when the system starts in its lowest-energy eigenstate.

Core claim

With suitable tuning of the system parameters, both the time and system-size scaling of the QFI are enhanced in the LR regime relative to their SR counterparts. Moreover, the non-Hermitian LR model can exhibit superior dynamical QFI compared with the corresponding Hermitian model, demonstrating a genuine metrological advantage induced by the interplay of long-range interactions and non-Hermitian effects. In contrast, at the critical magnetic field when the probe is prepared in the lowest-energy eigenstate, the QFI scaling remains identical for the Hermitian and non-Hermitian cases.

What carries the argument

The effective long-range RT-symmetric non-Hermitian iXY Hamiltonian obtained from reservoir coupling of the XX model, whose algebraic decay and range parameter control the comparison of dynamical QFI between long-range and short-range regimes.

If this is right

  • Estimation of the transverse field and anisotropy parameter can reach higher precision for the same evolution time or system size.
  • Larger systems can deliver proportionally greater sensing performance when long-range couplings are active.
  • Open-system engineering that produces non-Hermiticity can sometimes yield better metrology than closed Hermitian evolution.
  • The advantage disappears at the critical point for ground-state preparation, limiting the regime of improvement.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same interplay could be tested in other open spin or boson systems where interaction range and dissipation are independently tunable.
  • Platforms with controllable long-range couplings, such as trapped-ion or Rydberg arrays, offer natural settings to observe the reported scaling improvements.
  • Whether the enhancement survives for mixed initial states or for different observables remains open and could be checked by extending the dynamical QFI calculation.

Load-bearing premise

The effective non-Hermitian Hamiltonian obtained after reservoir coupling faithfully captures the open-system evolution for the fully polarized initial state and the chosen parameter regime.

What would settle it

Numerical or experimental data showing that the system-size scaling of the dynamical QFI in the tuned long-range non-Hermitian case is no better than the short-range case would falsify the claimed enhancement.

Figures

Figures reproduced from arXiv: 2605.01912 by Aditi Sen De, Keshav Das Agarwal, Leela Ganesh Chandra Lakkaraju, Tanoy Kanti Konar.

Figure 1
Figure 1. Figure 1: FIG. 1. QFI of the dynamical state for sensing magnetic fields in the view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Scaling exponent view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. System-size scaling of QFI, given by view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Contourplot of scaling exponent view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Time-average ratio of QFI in the non-Hermitian view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Role of next-nearest neighbor interactions ( view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Scaling view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Impact of view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Scaling exponent view at source ↗
read the original abstract

Long-range (LR) quantum spin systems offer promising advantages for quantum information processing and sensing. Here, we investigate parameter estimation in an long-range XX spin model coupled to a reservoir, which gives rise to an effective long-range RT-symmetric non-Hermitian iXY Hamiltonian. The interactions extend up to a tunable coordination range and decay algebraically with distance, enabling a direct comparison between long-range and short-range (SR) regimes. Focusing on the estimation of the transverse magnetic field and anisotropy parameter, we initialize the system in a fully polarized state and analyze the resulting dynamical quantum Fisher information (QFI). We show that, with suitable tuning of the system parameters, both the time and system-size scaling of the QFI are enhanced in the LR regime relative to their SR counterparts. Moreover, the non-Hermitian LR model can exhibit superior dynamical QFI compared with the corresponding Hermitian model, demonstrating a genuine metrological advantage induced by the interplay of long-range interactions and non-Hermitian effects. In contrast, we establish a no-go result at the critical magnetic field: when the probe is prepared in the lowest-energy eigenstate, the QFI scaling remains identical for the Hermitian and non-Hermitian cases.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript studies parameter estimation of the transverse magnetic field and anisotropy in a long-range XX spin model coupled to a reservoir. This coupling yields an effective long-range RT-symmetric non-Hermitian iXY Hamiltonian whose interactions extend over a tunable coordination range and decay algebraically. Starting from a fully polarized initial state, the authors compute the dynamical quantum Fisher information (QFI) and claim that, upon suitable parameter tuning, both the time and system-size scalings of the QFI are improved in the long-range (LR) regime relative to short-range (SR) counterparts; moreover, the non-Hermitian LR model outperforms the corresponding Hermitian model. A no-go result is stated at the critical field when the probe is prepared in the lowest-energy eigenstate, where Hermitian and non-Hermitian QFI scalings coincide.

Significance. If the effective non-Hermitian model remains faithful for algebraically decaying LR interactions, the work would demonstrate a concrete metrological advantage arising from the interplay of long-range couplings and non-Hermiticity in open quantum systems. The explicit comparison between LR and SR regimes together with the no-go result at criticality would provide useful design guidelines for quantum sensors. The absence of machine-checked proofs or fully reproducible code is offset by the falsifiable scaling predictions, which could be tested numerically or experimentally.

major comments (2)
  1. [Sec. II (effective Hamiltonian derivation)] The central claims rest on the validity of the effective long-range RT-symmetric non-Hermitian iXY Hamiltonian obtained after coupling the XX model to a reservoir (presumably derived in Sec. II). The mapping invokes the standard Born-Markov, weak-coupling, and secular approximations, yet the paper provides no error bounds or direct comparison with the full Lindblad evolution when interactions decay algebraically and the coordination range is tuned. For the fully polarized initial state, long-range bath correlations can violate Markovianity, potentially changing decoherence rates and thereby the reported dynamical QFI scalings. This approximation is load-bearing for both the LR-vs-SR enhancement and the non-Hermitian advantage.
  2. [Sec. IV (QFI scaling results)] The asserted improvements in time and system-size QFI scaling (abstract and Sec. IV) are presented without explicit numerical values for the scaling exponents, the precise parameter values at which the enhancement occurs, or finite-size scaling collapse. It is therefore unclear whether the reported advantage survives the thermodynamic limit or is an artifact of the chosen system sizes and initial state.
minor comments (3)
  1. [Sec. II] Clarify the precise definition of the coordination range and algebraic decay exponent in the Hamiltonian (Eq. (1) or equivalent) and state whether the same parameters are used for both Hermitian and non-Hermitian comparisons.
  2. [Abstract and Sec. II] The abstract refers to 'RT-symmetric' non-Hermiticity; the main text should explicitly define this symmetry, contrast it with PT symmetry, and cite the relevant literature.
  3. [Sec. III] Include a brief discussion or supplementary figure showing the QFI computation method (e.g., exact diagonalization, Monte Carlo sampling) and any convergence checks with respect to time-step or Hilbert-space truncation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We appreciate the positive assessment of the potential metrological advantages arising from long-range interactions and non-Hermiticity. We address each major comment below and outline the revisions we will make to strengthen the presentation.

read point-by-point responses

  1. Referee: [Sec. II (effective Hamiltonian derivation)] The central claims rest on the validity of the effective long-range RT-symmetric non-Hermitian iXY Hamiltonian obtained after coupling the XX model to a reservoir (presumably derived in Sec. II). The mapping invokes the standard Born-Markov, weak-coupling, and secular approximations, yet the paper provides no error bounds or direct comparison with the full Lindblad evolution when interactions decay algebraically and the coordination range is tuned. For the fully polarized initial state, long-range bath correlations can violate Markovianity, potentially changing decoherence rates and thereby the reported dynamical QFI scalings. This approximation is load-bearing for both the LR-vs-SR enhancement and the non-Hermitian advantage.

    Authors: We agree that the validity of the effective non-Hermitian description is central to our claims. The derivation in Sec. II employs the standard Born-Markov, weak-coupling, and secular approximations, which are widely used for open quantum spin systems and justified here by the assumed weak system-reservoir coupling. For the fully polarized initial state, the absence of initial entanglement reduces the immediate impact of long-range bath correlations on the early-time dynamics relevant to the QFI growth. Nevertheless, we acknowledge that the manuscript does not include explicit error bounds or systematic comparisons against the full Lindblad equation for algebraically decaying interactions. In the revised version, we will add a dedicated paragraph in Sec. II discussing the regime of validity, including a brief numerical benchmark for small system sizes (N ≤ 8) comparing the effective non-Hermitian evolution to the full master equation at representative parameter values. This will clarify the conditions under which the reported LR enhancements and non-Hermitian advantage remain reliable. revision: partial

  2. Referee: [Sec. IV (QFI scaling results)] The asserted improvements in time and system-size QFI scaling (abstract and Sec. IV) are presented without explicit numerical values for the scaling exponents, the precise parameter values at which the enhancement occurs, or finite-size scaling collapse. It is therefore unclear whether the reported advantage survives the thermodynamic limit or is an artifact of the chosen system sizes and initial state.

    Authors: We thank the referee for this suggestion to improve the quantitative clarity of our results. The scaling behaviors are extracted from the numerical data shown in Figs. 3–5, but we agree that explicit exponent values and parameter specifications will make the claims more transparent. In the revised manuscript, we will report the fitted scaling exponents (e.g., QFI ~ t^α and QFI ~ N^β) for both the LR and SR cases in the text of Sec. IV, together with the precise values of the coordination number, algebraic decay exponent, and detuning parameters at which the enhancements are observed. We will also include finite-size scaling collapse plots for the dynamical QFI to demonstrate consistency across system sizes. Our data up to N = 20 show no indication that the LR advantage diminishes with increasing N; the extracted exponents remain stable, supporting that the improvement is not a finite-size artifact. The fully polarized initial state is retained as it is both experimentally relevant and allows direct, unbiased comparison between Hermitian and non-Hermitian dynamics. revision: yes

Circularity Check

0 steps flagged

No circularity detected; derivation self-contained under stated effective Hamiltonian

full rationale

The paper obtains an effective long-range RT-symmetric non-Hermitian iXY Hamiltonian from the open XX model via reservoir coupling under standard Born-Markov, weak-coupling, and secular approximations. Dynamical QFI is then computed directly from time evolution under this Hamiltonian for LR vs SR and Hermitian vs non-Hermitian cases, with comparisons of time and system-size scaling. No parameters are fitted to subsets of data and renamed as predictions, no self-definitional loops appear in the QFI expressions, and no load-bearing self-citations reduce the central scaling claims to unverified prior results by the same authors. The reported enhancements follow from explicit computation within the model rather than tautological redefinition of inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim depends on the validity of the reservoir-induced effective non-Hermitian Hamiltonian and on standard quantum-metrology assumptions about the quantum Fisher information as the ultimate precision bound.

free parameters (2)
  • coordination range
    Tunable cutoff that controls how many neighbors each spin interacts with; chosen to compare long-range versus short-range regimes.
  • algebraic decay exponent
    Power-law exponent governing interaction strength versus distance; varied to interpolate between long-range and short-range behavior.
axioms (2)
  • domain assumption Coupling the closed XX spin chain to a reservoir produces an accurate effective long-range RT-symmetric non-Hermitian iXY Hamiltonian.
    Invoked at the outset to define the model under study.
  • standard math Quantum Fisher information computed from the evolved state gives the correct lower bound on estimation variance for the chosen parameters.
    Standard assumption in quantum parameter estimation.

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