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arxiv: 2308.01036 · v4 · submitted 2023-08-02 · 🪐 quant-ph

Performance Analysis of Satellite-Based QKD Protocols

Muskan , Ramniwas Meena , Subhashish Banerjee This is my paper

Pith reviewed 2026-05-24 07:16 UTC · model grok-4.3

classification 🪐 quant-ph
keywords satellite QKDquantum key distributionBB84 protocolB92 protocolBBM92 protocolE91 protocolQBERuplink downlink
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The pith

Downlink LEO satellite links achieve lower QBER and higher secure key rates than uplinks for BB84, B92, BBM92, and E91.

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

The paper models QBER and secure key rates for four QKD protocols over LEO satellite links in uplink and downlink directions. It applies a Gaussian beam model that accounts for diffraction, pointing errors, atmospheric turbulence, and background noise under day and night conditions while varying zenith angle. The central result is that downlinks outperform uplinks overall, BB84 beats B92 in prepare-and-measure schemes, and BBM92 beats E91 in entanglement-based schemes.

Core claim

Downlink links generally exhibit lower QBER and higher secure key rates than uplinks, and among prepare-and-measure schemes, BB84 consistently outperforms B92, while in entanglement-based approaches, BBM92 achieves higher key rates than E91.

What carries the argument

Gaussian beam formalism modeling the optical link with diffraction, pointing errors, atmospheric turbulence, and background noise contributions.

If this is right

  • Downlink paths are preferred for satellite-based secure key distribution to maximize rates.
  • BB84 is the stronger choice among prepare-and-measure protocols for satellite use.
  • BBM92 is the stronger choice among entanglement-based protocols for satellite use.
  • Performance degrades with increasing zenith angle and differs between day and night due to noise and turbulence.

Where Pith is reading between the lines

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

  • Network designers could prioritize downlink geometry when planning constellations for global QKD coverage.
  • The protocol rankings may inform choices in hybrid satellite-terrestrial quantum networks.
  • Extending the model to higher orbits or additional turbulence regimes could test whether the downlink advantage persists.

Load-bearing premise

The Gaussian beam model of the optical link, including diffraction, pointing errors, turbulence, and noise, is accurate enough for the LEO uplink and downlink cases studied.

What would settle it

An experimental measurement on actual LEO satellite QKD links that shows uplink QBER lower than downlink or B92 outperforming BB84 under the modeled conditions.

Figures

Figures reproduced from arXiv: 2308.01036 by Muskan, Ramniwas Meena, Subhashish Banerjee.

Figure 1
Figure 1. Figure 1: Measurements directions for the Ekert protocol. The measurements are depicted in the [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) Plot for transmittance with zenith angle for uplink night-time, (b) Plot for transmit [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) Plot for QBER and keyrate for BB84 protocol with zenith angle for uplink night-time, [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) Plot for QBER and keyrate for B92 protocol with zenith angle for uplink night-time, [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) Plot for QBER and keyrate for BBM92 protocol with zenith angle for uplink night [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: (a)Plot for QBER and keyrate for E91 protocol with zenith angle for uplink night-time, [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
read the original abstract

Satellite-based free-space quantum key distribution (QKD) provides a practical framework for achieving secure global communication beyond the limitations of optical fibers. In this work, the quantum bit error rate (QBER) and secure key rate of four representative protocols-BB84, B92, BBM92, and E91 are investigated over low earth orbit (LEO) links in both uplink and downlink configurations. The optical link is modeled using a Gaussian beam formalism, incorporating the effects of diffraction, pointing errors, atmospheric turbulence, and background noise contributions. The protocols are examined under day and night-time operating conditions, and their dependence on the zenith angle is analyzed. The findings show that downlink links generally exhibit lower QBER and higher secure key rates than uplinks, and among prepare-and-measure schemes, BB84 consistently outperforms B92, while in entanglement-based approaches, BBM92 achieves higher key rates than E91.

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 performance of four QKD protocols (BB84, B92, BBM92, and E91) over LEO satellite free-space links in uplink and downlink configurations. It employs a Gaussian beam model incorporating diffraction, pointing errors, atmospheric turbulence, and background noise to compute QBER and secure key rates under day/night conditions as a function of zenith angle. The central claims are that downlinks exhibit lower QBER and higher key rates than uplinks, BB84 outperforms B92 among prepare-and-measure schemes, and BBM92 outperforms E91 among entanglement-based schemes.

Significance. If the link model is accurate, the comparative results offer practical guidance for protocol selection and link configuration in satellite QKD deployments. The side-by-side treatment of prepare-and-measure and entanglement-based protocols under realistic LEO conditions addresses a relevant systems-level question.

major comments (2)
  1. [§3] §3 (optical link model): the uplink/downlink asymmetry in QBER and key rate rests on the turbulence component correctly reproducing stronger scintillation and beam wander for uplinks (full atmospheric path) versus downlinks (turbulence localized near the receiver). The manuscript must specify the exact C_n^2 profile, turbulence spectrum (e.g., Kolmogorov or von Kármán), and zenith-angle dependence used; without this, the reported ordering cannot be verified as robust rather than an artifact of the chosen functional forms.
  2. [§4–5] §4–5 (results): the abstract states headline comparisons but the results sections provide no tabulated numerical values, error bars, or sensitivity analysis for QBER and key rates across the four protocols. This absence prevents assessment of whether the claimed ordering (downlink > uplink, BB84 > B92, BBM92 > E91) remains stable under reasonable variations in pointing jitter or background noise.
minor comments (2)
  1. [§2] Notation for the secure key rate formula should be defined explicitly before its first use; the dependence on the sifting factor and error-correction efficiency is not stated in the abstract or early sections.
  2. [Figures 3–6] Figure captions for the QBER vs. zenith-angle plots should include the specific day/night background photon rates and the assumed receiver aperture diameter.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and helpful comments on our manuscript. We address the major comments point by point below and plan to revise the manuscript to incorporate the suggested improvements.

read point-by-point responses

  1. Referee: [§3] §3 (optical link model): the uplink/downlink asymmetry in QBER and key rate rests on the turbulence component correctly reproducing stronger scintillation and beam wander for uplinks (full atmospheric path) versus downlinks (turbulence localized near the receiver). The manuscript must specify the exact C_n^2 profile, turbulence spectrum (e.g., Kolmogorov or von Kármán), and zenith-angle dependence used; without this, the reported ordering cannot be verified as robust rather than an artifact of the chosen functional forms.

    Authors: We agree that the specific details of the turbulence model are required to verify the results. We will revise §3 to explicitly provide the C_n^2 profile, the turbulence spectrum, and the zenith-angle dependence used in our calculations. revision: yes

  2. Referee: [§4–5] §4–5 (results): the abstract states headline comparisons but the results sections provide no tabulated numerical values, error bars, or sensitivity analysis for QBER and key rates across the four protocols. This absence prevents assessment of whether the claimed ordering (downlink > uplink, BB84 > B92, BBM92 > E91) remains stable under reasonable variations in pointing jitter or background noise.

    Authors: We acknowledge that the presentation of results would benefit from tabulated data and sensitivity analysis. In the revised manuscript, we will add tables listing the computed QBER and secure key rate values for key zenith angles in both day and night conditions for all four protocols in uplink and downlink configurations. We will also include a sensitivity analysis showing how the protocol ordering holds under variations in pointing jitter and background noise levels. revision: yes

Circularity Check

0 steps flagged

No circularity: standard link model yields protocol comparisons

full rationale

The paper propagates four QKD protocols through an explicit Gaussian-beam link model that incorporates diffraction, pointing errors, turbulence, and noise. The reported orderings (downlink better than uplink; BB84 > B92; BBM92 > E91) are direct numerical outputs of that model under stated conditions, not quantities defined in terms of themselves or obtained by fitting a subset and relabeling the result. No equations, self-citations, or ansatzes are shown to reduce the central claims to their inputs by construction. The derivation chain is therefore self-contained against external physical benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The analysis rests on the domain assumption that the chosen Gaussian-beam plus turbulence model is representative; no free parameters or invented entities are visible in the abstract.

axioms (1)
  • domain assumption Gaussian beam formalism incorporating diffraction, pointing errors, atmospheric turbulence, and background noise accurately represents LEO satellite optical links.
    Explicitly invoked in the abstract as the basis for computing QBER and key rates.

pith-pipeline@v0.9.0 · 5680 in / 1238 out tokens · 25456 ms · 2026-05-24T07:16:30.780346+00:00 · methodology

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Reference graph

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