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arxiv: 2501.06484 · v3 · submitted 2025-01-11 · 🪐 quant-ph · gr-qc

Resilience of Quantum Teleportation Fidelity for Bipartite Mixed States near Schwarzschild and Dilaton Black Holes

Abhijit Mandal , Sovik Roy This is my paper

Pith reviewed 2026-05-23 05:31 UTC · model grok-4.3

classification 🪐 quant-ph gr-qc
keywords quantum teleportationblack holesHawking radiationentangled statesGHZ stateW statefidelityDirac fields
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The pith

Teleportation fidelity stays above the classical threshold for W-class states but falls below it for GHZ states near black hole horizons.

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

The paper examines how tripartite entangled states degrade into bipartite mixed channels when two observers approach a black hole horizon while the third stays in flat space. It applies quantization of Dirac fields and Bogoliubov transformations to compute the resulting teleportation fidelity in both Schwarzschild and GHS dilaton geometries. The central finding is that fidelity remains above two thirds for channels from W-class states but drops below that value for channels from GHZ states. A sympathetic reader would care because the result distinguishes which initial entanglement resources could still support quantum communication tasks in strong gravitational fields.

Core claim

After tracing out one observer, the bipartite channels obtained from W-class tripartite states retain teleportation fidelity above the classical bound of 2/3 near both Schwarzschild and GHS dilaton black holes, while the corresponding channels from GHZ states fall below this bound, even though entanglement degrades in both cases due to Hawking radiation.

What carries the argument

Bogoliubov transformations on quantized Dirac fields that produce the final bipartite mixed states from the initial tripartite GHZ or W-class states after one observer is traced out.

If this is right

  • Teleportation remains feasible near event horizons when the initial state is of W-class type.
  • GHZ-derived channels lose their quantum advantage for teleportation in the same curved-spacetime setting.
  • The survival of useful bipartite entanglement depends on the entanglement class of the starting tripartite state.
  • Hawking radiation affects the two classes of states differently with respect to their utility for quantum information tasks.

Where Pith is reading between the lines

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

  • W-class states may prove more suitable than GHZ states for maintaining quantum communication links near compact objects.
  • The distinction between state classes could guide preparation of resources for proposed tests in analog gravity systems.
  • Similar class-dependent resilience might appear in other protocols such as quantum key distribution performed near black holes.

Load-bearing premise

The Bogoliubov transformations applied to the Dirac fields correctly capture how the black hole spacetime mixes the modes and degrades the initial states into the final bipartite channels.

What would settle it

An explicit calculation of the teleportation fidelity for a W-class derived channel at a chosen black hole mass or dilaton parameter that returns a value below 2/3.

Figures

Figures reproduced from arXiv: 2501.06484 by Abhijit Mandal, Sovik Roy.

Figure 1
Figure 1. Figure 1: The schematic diagram shows that the 3 qubit states being exposed near the event horizon of the black hole. [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: We plot the tangle of the GHZ state against monochromatic frequency (ω) and Hawking temperature (T). Fig.(A) shows the variation of tangle τ (ρ wfabc GHZ ) when Hawking temperature (T) is varied from 0 to 10 and monochromatic frequency (ω) is varied from 0 to 900 in the backdrop of Schwarzschild black hole. Fig.(B) shows the variation of same τ (ρ wfabc GHZ ) when charge (Q) is varied from 0 to 20 and mono… view at source ↗
Figure 3
Figure 3. Figure 3: Variation of concurrence of bipartite mixed states [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Variation of concurrence of bipartite mixed states [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Variation of teleportation fidelity of bipartite mixed states [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Variation of teleportation fidelity of bipartite mixed states [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Variation of concurrence of bipartite mixed states [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Variation of concurrence of bipartite mixed states [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Variation of concurrence of bipartite mixed states [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Variation of concurrence of bipartite mixed states [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
read the original abstract

We investigate the robustness of quantum teleportation in the presence of strong gravitational fields by analysing bipartite mixed states derived from tripartite GHZ and W-class states near black hole event horizons. Considering a scenario where two observers approach the horizon of either a Schwarzschild or a Garfinkle Horowitz Strominger (GHS) Dilaton black hole while a third remains in flat space, we quantify the teleportation fidelity of the resulting bipartite channels after tracing out one party. Through the quantization of Dirac fields and Bogoliubov transformations, we compute the teleportation fidelity under the influence of Hawking radiation and spacetime curvature. Our results show that while entanglement degrades, teleportation fidelity remains above the classical threshold of $f>\frac{2}{3}$ for channels derived from W-class states, but not for GHZ-derived states. This indicates that quantum teleportation can remain feasible near black holes provided the initial entangled state retains useful bipartite entanglement.

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 manuscript analyzes the teleportation fidelity of bipartite mixed states obtained by tracing one observer from tripartite GHZ and W-class states, where two observers approach the horizon of a Schwarzschild or GHS dilaton black hole. Dirac fields are quantized and Bogoliubov transformations are applied to incorporate Hawking radiation effects; the resulting fidelities are reported to remain above the classical threshold f > 2/3 for W-class-derived channels but fall below it for GHZ-derived channels.

Significance. If the numerical results hold, the work shows that entanglement class determines resilience of teleportation under gravitational decoherence, providing a concrete distinction between GHZ and W states in curved-spacetime quantum information tasks. The reliance on standard Bogoliubov techniques for Dirac fields in black-hole backgrounds is a methodological strength, though the findings remain specific to the chosen vacua and tracing procedure.

major comments (2)
  1. [Results / fidelity computation section] The central claim rests on the reduced bipartite density operators obtained after Bogoliubov transformation and tracing. The manuscript must supply the explicit matrix elements of these operators (or the fidelity formula in terms of the Bogoliubov coefficients) for both GHZ and W states; without them the reported threshold crossing cannot be independently verified and the off-diagonal coherence degradation remains opaque.
  2. [Methods / Bogoliubov transformation subsection] The choice of which observer is traced and the specific positive/negative frequency mode definitions enter the final fidelity values. The paper should state the precise vacuum (Unruh or Hartle-Hawking) and the numerical ranges of the surface gravity or dilaton parameter at which the W-class fidelity stays above 2/3 while the GHZ fidelity does not.
minor comments (2)
  1. Figure captions should explicitly label the curves corresponding to Schwarzschild versus GHS backgrounds and to GHZ versus W initial states.
  2. [Abstract] The abstract states the threshold result but omits the range of black-hole parameters or the number of modes retained; adding these would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the recommendation for major revision. We address each major comment below and will revise the manuscript to supply the requested explicit expressions, clarifications, and numerical details.

read point-by-point responses

  1. Referee: [Results / fidelity computation section] The central claim rests on the reduced bipartite density operators obtained after Bogoliubov transformation and tracing. The manuscript must supply the explicit matrix elements of these operators (or the fidelity formula in terms of the Bogoliubov coefficients) for both GHZ and W states; without them the reported threshold crossing cannot be independently verified and the off-diagonal coherence degradation remains opaque.

    Authors: We agree that the explicit matrix elements are required for independent verification. In the revised manuscript we will add the full 4x4 reduced density matrices for the GHZ-derived and W-class-derived channels, written explicitly in terms of the Bogoliubov coefficients that arise after the mode transformations and the partial trace. We will also present the teleportation fidelity formula directly in terms of those coefficients so that the suppression of the off-diagonal coherences is transparent. revision: yes

  2. Referee: [Methods / Bogoliubov transformation subsection] The choice of which observer is traced and the specific positive/negative frequency mode definitions enter the final fidelity values. The paper should state the precise vacuum (Unruh or Hartle-Hawking) and the numerical ranges of the surface gravity or dilaton parameter at which the W-class fidelity stays above 2/3 while the GHZ fidelity does not.

    Authors: The calculations employ the Hartle-Hawking vacuum for the Dirac fields in both the Schwarzschild and GHS dilaton geometries; the observer traced out is the one that remains in the asymptotically flat region. We will state these choices explicitly in the methods section. In addition, we will report the concrete numerical intervals of surface gravity and dilaton charge for which the W-class fidelity remains above 2/3 while the GHZ-derived fidelity drops below the threshold, as obtained from our numerical evaluation of the fidelity expressions. revision: yes

Circularity Check

0 steps flagged

No circularity; standard Bogoliubov + fidelity computation is self-contained

full rationale

The derivation applies established quantization of Dirac fields, Bogoliubov transformations between asymptotic and near-horizon modes, and the standard teleportation fidelity formula to the reduced bipartite density operators obtained by tracing one observer. These steps are independent calculations from the initial tripartite GHZ/W states and the metric; no parameter is fitted to the target fidelity, no result is renamed as a prediction, and no load-bearing premise rests on self-citation. The reported distinction (W-class above 2/3, GHZ below) follows directly from the explicit matrix elements after tracing, without reduction to the inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard quantization of Dirac fields in curved spacetime and the validity of the Bogoliubov transformation between inertial and accelerated observers; no free parameters, ad-hoc axioms, or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Dirac fields can be quantized in Schwarzschild and GHS dilaton geometries using standard Bogoliubov transformations between asymptotic observers.
    Invoked when the abstract states 'through the quantization of Dirac fields and Bogoliubov transformations' to obtain the mixed states.

pith-pipeline@v0.9.0 · 5693 in / 1280 out tokens · 23829 ms · 2026-05-23T05:31:13.795868+00:00 · methodology

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Reference graph

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