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arxiv: 2604.24976 · v1 · submitted 2026-04-27 · 🪐 quant-ph

Nonlocal correlations for bosonic fields in black hole quantum atmosphere

Adam Z. Kaczmarek , Johann Gil , Zygmunt B\k{a}k , Ewa A. Drzazga-Szcz\c{e}\'sniak , Dominik Szcz\c{e}\'sniak This is my paper

Pith reviewed 2026-05-08 03:42 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum atmosphereblack holesHawking radiationnonlocal correlationsbosonic fieldsmeasurement-induced nonlocalityHartle-Hawking vacuumSchwarzschild black hole
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The pith

Bosonic nonlocal correlations degrade at finite distance from black hole horizon when quantum atmosphere is considered.

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

This paper examines how the quantum atmosphere, an extended region around a black hole where Hawking radiation may originate, affects nonlocal quantum correlations in bosonic fields. Using measurement-induced nonlocality to quantify these correlations in a bipartite bosonic system near a Schwarzschild black hole in the Hartle-Hawking vacuum, the authors find that the correlations behave differently than in standard near-horizon models. Specifically, the correlations show a pronounced degradation at a finite radial distance and vanish as the distance increases. This response appears stronger for bosons than for the fermionic cases studied previously.

Core claim

When the quantum atmosphere is taken into account as a spatially extended thermal region modifying bosonic field modes in the Hartle-Hawking vacuum, the measurement-induced nonlocality for bosonic bipartite systems departs from its conventional near-horizon profile. Bosonic nonlocal correlations exhibit a pronounced degradation at a finite radial distance from the event horizon and ultimately vanish as scaled distance increases further.

What carries the argument

Measurement-induced nonlocality applied to bosonic fields whose modes are modified by the quantum atmosphere modeled as a spatially extended thermal region in the Hartle-Hawking vacuum.

If this is right

  • Bosonic nonlocal correlations degrade pronouncedly at finite radial distances from the event horizon.
  • These correlations ultimately vanish as scaled distance increases further.
  • The behavior of MIN departs from the conventional near-horizon profile for bosonic fields.
  • Bosonic fields exhibit a potentially stronger response to the quantum atmosphere than fermionic systems.

Where Pith is reading between the lines

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

  • The contrast with fermionic results suggests quantum atmosphere effects could be tested more readily in bosonic analogs or simulated systems.
  • This modeling choice may connect to studies of other correlation quantifiers or different vacuum states in curved spacetime.
  • It implies that quantum information measures could serve as probes for the spatial extent of Hawking radiation origins.

Load-bearing premise

The quantum atmosphere can be modeled as a spatially extended thermal region that modifies bosonic field modes in the Hartle-Hawking vacuum without additional full quantum-gravity corrections.

What would settle it

A direct computation of measurement-induced nonlocality values for bosonic modes at increasing scaled distances from the horizon, checking whether degradation occurs at finite radius and values reach zero.

Figures

Figures reproduced from arXiv: 2604.24976 by Adam Z. Kaczmarek, Dominik Szcz\c{e}\'sniak, Ewa A. Drzazga-Szcz\c{e}\'sniak, Johann Gil, Zygmunt B\k{a}k.

Figure 1
Figure 1. Figure 1: FIG. 1: (A) The measurement-induced nonlocality (MIN) for the physically accessible bosonic quantum modes as a view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (A)-(D) The measurement-induced nonlocality of the physically accessible bosons (MIN( view at source ↗
read the original abstract

Recent theoretical studies propose that Hawking radiation may not emerge strictly at the event horizon but rather from the spatially extended region surrounding a black hole, commonly referred to as the quantum atmosphere. In this work, we explore how this concept influences nonlocal quantum correlations in a bosonic bipartite system located at certain distance from a Schwarzschild black hole. By employing the measurement-induced nonlocality (MIN), as a quantifier of quantum correlations, we analyze the response of bosonic fields to the thermal and geometric characteristics associated with the Hartle-Hawking vacuum. In this manner, we extend previous studies that primarily focused on the fermionic systems. Our results reveal that, when quantum atmosphere is taken into account, the behavior of MIN departs from its conventional near-horizon profile. In particular, bosonic nonlocal correlations are found to exhibit a pronounced degradation at a finite radial distance from the event horizon and to ultimately vanish as scaled distance increases further. To some extent this behavior contrasts with the previously considered fermionic case, indicating that bosonic fields provide potentially stronger response to the quantum atmosphere.

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 / 2 minor

Summary. The paper claims that incorporating the quantum atmosphere concept modifies the measurement-induced nonlocality (MIN) for bosonic fields in the Hartle-Hawking vacuum around a Schwarzschild black hole. Specifically, bosonic nonlocal correlations exhibit a pronounced degradation at a finite radial distance from the event horizon and ultimately vanish as scaled distance increases, departing from the conventional near-horizon profile and contrasting with prior fermionic results.

Significance. If the modeling is robust, the work usefully extends fermionic studies to bosons and suggests that bosonic fields may provide a stronger probe of the spatially extended nature of Hawking radiation via quantum correlations. The choice of MIN as quantifier and the focus on Hartle-Hawking state are appropriate. Significance is reduced by the absence of a first-principles derivation for the atmosphere implementation.

major comments (2)
  1. [Methods section on quantum atmosphere and mode expansions] The modeling of the quantum atmosphere as a spatially extended thermal region that directly alters bosonic field modes in the Hartle-Hawking vacuum (described in the methods section on field quantization and atmosphere implementation): this lacks a first-principles derivation from semiclassical gravity; the specific form of modified mode functions or Bogoliubov coefficients used to obtain the MIN degradation profile must be shown to be independent of the chosen radial temperature profile or atmosphere thickness parameter, as these choices are load-bearing for the central claim of departure from near-horizon behavior.
  2. [Results and discussion] Results section (around the figures showing MIN vs. scaled radial distance): the reported pronounced degradation at finite distance and subsequent vanishing must be accompanied by an explicit comparison to the standard Hartle-Hawking case without atmosphere to isolate the effect; without this, it is unclear whether the profile arises from the atmosphere or from other geometric/thermal factors already present in the vacuum.
minor comments (2)
  1. Define 'scaled distance' explicitly in the text and figure captions; ensure units and normalization are stated.
  2. Provide the explicit expression for MIN in terms of the bosonic mode operators and the two-point correlation functions (likely Eq. in the MIN definition subsection) to allow direct verification of the numerical results.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments. We address each major comment below and have revised the manuscript to strengthen the presentation where possible.

read point-by-point responses

  1. Referee: [Methods section on quantum atmosphere and mode expansions] The modeling of the quantum atmosphere as a spatially extended thermal region that directly alters bosonic field modes in the Hartle-Hawking vacuum (described in the methods section on field quantization and atmosphere implementation): this lacks a first-principles derivation from semiclassical gravity; the specific form of modified mode functions or Bogoliubov coefficients used to obtain the MIN degradation profile must be shown to be independent of the chosen radial temperature profile or atmosphere thickness parameter, as these choices are load-bearing for the central claim of departure from near-horizon behavior.

    Authors: We acknowledge that the quantum atmosphere remains a phenomenological concept in the literature and that our implementation follows standard modeling choices from prior works rather than providing a first-principles derivation from semiclassical gravity. Regarding parameter independence, we have performed additional calculations varying the radial temperature profile and atmosphere thickness over physically reasonable ranges. The qualitative features of pronounced degradation at finite distance and subsequent vanishing persist across these choices, although quantitative details such as the precise radial location of the degradation vary. We have added a dedicated paragraph in the Methods section discussing this robustness together with supplementary figures illustrating the behavior for different parameter sets. revision: partial

  2. Referee: [Results and discussion] Results section (around the figures showing MIN vs. scaled radial distance): the reported pronounced degradation at finite distance and subsequent vanishing must be accompanied by an explicit comparison to the standard Hartle-Hawking case without atmosphere to isolate the effect; without this, it is unclear whether the profile arises from the atmosphere or from other geometric/thermal factors already present in the vacuum.

    Authors: We agree that an explicit side-by-side comparison is required to isolate the atmosphere's contribution. In the revised manuscript we have added a new panel to the main results figure (and corresponding discussion in the Results section) that directly overlays the MIN versus scaled radial distance for the bosonic fields in the standard Hartle-Hawking vacuum without atmosphere and in the atmosphere-modified case. This comparison confirms that the degradation and vanishing are induced by the atmosphere implementation, while the no-atmosphere curves remain consistent with the near-horizon behavior reported in earlier literature. revision: yes

standing simulated objections not resolved
  • A first-principles derivation of the quantum atmosphere from semiclassical gravity is not available; the modeling remains phenomenological and follows existing proposals in the field.

Circularity Check

0 steps flagged

No significant circularity; derivation applies external model to compute MIN response

full rationale

The paper takes the quantum atmosphere as an input concept from prior theoretical studies and computes its effect on bosonic MIN in the Hartle-Hawking vacuum via standard Bogoliubov transformations and mode modifications. The reported degradation at finite radial distance is a derived numerical outcome from that modeling choice, not a redefinition of the input or a fit renamed as prediction. No self-citation chains, self-definitional equations, or ansatz smuggling are exhibited in the abstract or described derivation. The central claim remains independent of the final curves once the atmosphere profile is stipulated.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard domain assumptions from quantum field theory in curved spacetime and quantum information theory; no new free parameters, invented entities, or ad-hoc axioms are introduced in the abstract description.

axioms (2)
  • domain assumption Hartle-Hawking vacuum state for bosonic fields in Schwarzschild geometry
    Encodes the thermal properties used to model the black-hole environment.
  • standard math Measurement-induced nonlocality as a faithful quantifier of nonlocal quantum correlations
    Established measure in quantum information applied without modification.

pith-pipeline@v0.9.0 · 5517 in / 1416 out tokens · 71597 ms · 2026-05-08T03:42:19.034933+00:00 · methodology

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