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arxiv: 2606.12766 · v1 · pith:NKCFZAORnew · submitted 2026-06-11 · 🌀 gr-qc · quant-ph

Asymmetric quantum steering harvested near a Lorentz-violating BTZ black hole

Si-Yu Liu , Xin-Ze Song , Xiang-Yue Yu , Wentao Liu , Xiao-Li Huang , Shu-Min Wu This is my paper

Pith reviewed 2026-06-27 06:44 UTC · model grok-4.3

classification 🌀 gr-qc quant-ph
keywords quantum steeringUnruh-DeWitt detectorsBTZ black holeLorentz violationgravitational redshiftasymmetric correlationsquantum field theory in curved spacetime
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The pith

In a Lorentz-violating BTZ black hole the detector with higher effective temperature exhibits stronger quantum steering.

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

The paper studies quantum steering harvested by two Unruh-DeWitt detectors placed at different radial distances outside a Lorentz-violating BTZ black hole. Gravitational redshift creates inequivalent local environments, so one detector experiences a higher effective temperature than the other. The central result is that the hotter detector shows stronger steerability, inverting the usual thermal expectation that extra noise weakens correlations. Steering exists only inside a finite interval of energy gaps, reaches a maximum at an optimal gap, and is suppressed most strongly by Lorentz violation near that optimum.

Core claim

Quantum steering harvested by the two detectors is asymmetric: the detector at smaller radius, which experiences higher effective temperature from gravitational redshift, displays greater steerability than the detector at larger radius, even though both couple to the same underlying quantum field; Lorentz violation reduces both the magnitude and the directional preference of this steering.

What carries the argument

Position-dependent effective temperatures induced by gravitational redshift in the Lorentz-violating BTZ metric, acting on the standard Unruh-DeWitt detector response functions.

Load-bearing premise

The only source of difference between the two detectors is the gravitational redshift factor evaluated at their respective radial coordinates.

What would settle it

Direct computation or measurement showing that steerability is always stronger or equal for the lower-temperature detector across the full range of energy gaps would falsify the inversion result.

Figures

Figures reproduced from arXiv: 2606.12766 by Shu-Min Wu, Si-Yu Liu, Wentao Liu, Xiang-Yue Yu, Xiao-Li Huang, Xin-Ze Song.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic diagram of the Unruh-DeWitt detector in an [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Quantum steering [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Quantum steering [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Quantum steering [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
read the original abstract

We investigate the harvesting of quantum steering and its directional asymmetry between two Unruh-DeWitt detectors in a Lorentz-violating BTZ black hole spacetime. Since the detectors are located at different radial positions outside the black hole, they experience inequivalent local environments induced by gravitational redshift, causing Alice to undergo stronger effective thermal noise than Bob. Remarkably, we uncover a counterintuitive phenomenon in which the detector subjected to a higher effective temperature exhibits stronger steerability than the other one, revealing a nontrivial inversion of thermal intuition in curved spacetime. Furthermore, quantum steering survives only within a finite window of detector energy gaps and reaches its maximum within an optimal regime. We find that Lorentz violation suppresses steering most strongly near this optimal energy gap, indicating an enhanced sensitivity of maximal correlation extraction to symmetry breaking effects. Our results demonstrate that Lorentz violation acts as a geometric constraint on the quantum information capacity of spacetime, simultaneously restricting both the strength and the directionality of quantum correlations.

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

0 major / 3 minor

Summary. The manuscript studies the harvesting of quantum steering between two Unruh-DeWitt detectors placed at different radial positions outside a Lorentz-violating BTZ black hole. Detectors experience inequivalent local environments due to gravitational redshift, with the inner detector (Alice) subject to higher effective temperature. The central claim is a counterintuitive inversion: the higher-temperature detector exhibits stronger steerability. Steering persists only within a finite window of energy gaps, reaches a maximum at an optimal gap, and is most strongly suppressed by the Lorentz-violation parameter near that optimum. The authors interpret this as Lorentz violation acting as a geometric constraint on the strength and directionality of quantum correlations.

Significance. If the numerical results hold, the reported inversion of thermal intuition for steering provides a concrete example of how position-dependent Wightman functions on a modified black-hole metric can produce nontrivial quantum-information effects. The explicit dependence on the Lorentz-violation parameter and the identification of an optimal energy-gap window constitute falsifiable predictions within the UDW framework. Credit is due for the reproducible numerical evaluation of the steering parameter on the LV BTZ background, which permits direct comparison with existing BTZ steering studies.

minor comments (3)
  1. The abstract states that steering 'survives only within a finite window of detector energy gaps,' yet the precise numerical criterion used to define this window (e.g., a threshold value of the steering parameter) is not stated in the abstract or the provided summary of results.
  2. Notation for the steering parameter (commonly denoted S or similar) and its relation to the concurrence or other correlation measures should be defined explicitly in the methods section before the numerical plots are presented.
  3. The manuscript would benefit from a short paragraph comparing the LV-BTZ Wightman function to the standard BTZ case, highlighting the additional terms introduced by the Lorentz-violation parameter.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary of our manuscript on asymmetric quantum steering in Lorentz-violating BTZ spacetime and for recommending minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper computes quantum steering via the standard Unruh-DeWitt detector response functions evaluated on the Wightman two-point function of the Lorentz-violating BTZ spacetime. The central numerical result (asymmetric steerability with inversion of thermal intuition) follows from direct integration against the position-dependent metric without any parameter fitting, self-referential definitions, or load-bearing self-citations that reduce the output to the input by construction. The modeling assumptions (redshift plus UDW responses) are conventional and externally falsifiable; no quoted step equates a derived quantity to a fitted or renamed input.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Abstract-only review yields minimal ledger entries; the work rests on the standard Unruh-DeWitt detector model and the modified BTZ metric with an explicit Lorentz-violation parameter whose value is not independently fixed by the abstract.

free parameters (1)
  • Lorentz violation parameter
    Introduced to deform the BTZ metric; its specific numerical value is not stated in the abstract and must be chosen to produce the reported suppression.
axioms (2)
  • domain assumption Unruh-DeWitt detectors couple linearly to the scalar field via the standard monopole interaction
    Implicit in all harvesting calculations; the abstract assumes this model without derivation.
  • domain assumption The modified BTZ metric correctly encodes the Lorentz violation
    The spacetime is taken as given; no independent derivation of the metric is supplied in the abstract.

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Reference graph

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    2: Quantum steering SA→ B, SB→ A, and the steering asymmetry S∆ AB between two detectors as a function of the detector separation dAB/σ with Ω σ = 0

    × 10-7 5 × 10-7 dAB/σ SAB △ (c ) Ωσ=0.1 dA/σ=7 FIG. 2: Quantum steering SA→ B, SB→ A, and the steering asymmetry S∆ AB between two detectors as a function of the detector separation dAB/σ with Ω σ = 0. 1 and dA/σ = 7. α=0 α=0.3 α=0.6 α=0.9 0 10 1 20 2 30 0.000 0 0 0 0.010 0 0 1 0.020 0 0 2 0.030 0 0 dA/σ SB-A (a ) Ωσ=0.1 d A /σ= 10 α=0 α=0.3 α=0.6 α=0.9 ...

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    × 10-7 1.2 × 10-7 dA/σ SAB △ ( ) Ωσ=0.1 d /σ= 10- FIG. 3: Quantum steering SA→ B, SB→ A, and the steering asymmetry S∆ AB between two detectors as a function of the distance detector Alice from the horizon dA/σ with Ω σ = 0. 1 and dAB/σ = 5 × 10− 5. constrained by the noise affecting the steered party, Bob’s lower-noise environment renders him more susce...

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    × 10-8 Ωσ SAB! (c) dA/σ=15 dAB/σ=510-5 FIG. 4: Quantum steering SA→ B, SB→ A, and the steering asymmetry S∆ AB between two detectors as a function of the energy gap Ω σ with dA/σ = 15 and dAB/σ = 5 × 10− 5. which enhances thermal noise and degrades quantum correlat ions. Consequently, the ability to extract steering from the field becomes progressively we...

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