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arxiv: 2606.24431 · v1 · pith:IQZ6EJSWnew · submitted 2026-06-23 · 🪐 quant-ph

Free-Space CV-QKD with Single-Mode Fiber Reception: Effective Coupling Statistics and Protocol-Dependent Reference Noise

Hesham S. Ibrahim , Arnaud Coatanhay This is my paper

Pith reviewed 2026-06-26 00:00 UTC · model grok-4.3

classification 🪐 quant-ph
keywords free-space CV-QKDsingle-mode fiber receptionatmospheric turbulencecoupling efficiencypilot-assisted protocolsreference noiseGG02 protocolphase-screen model
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The pith

A scalar effective coupling law suffices for GG02 free-space CV-QKD but pilot-assisted protocols require an extra differential reference observable.

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

The paper models free-space CV-QKD reception into single-mode fiber by propagating signals through random phase screens that represent atmospheric turbulence, then collecting light at a finite aperture and projecting it onto the fiber mode. For the standard GG02 protocol it finds that the statistics of this coupling efficiency can be summarized by a single scalar law that yields an accurate Gaussian-channel model for key-rate calculations. When a transmitted pilot travels alongside the signal through correlated but non-identical turbulence, however, phase mismatch and loss of coherence after coupling introduce an additional reference-noise term that the coupling statistics alone cannot capture. The distinction shows that protocol choice determines how much detail about the turbulence must be retained at the receiver.

Core claim

Within the split-step phase-screen model, a scalar effective law for SMF coupling efficiency supplies an accurate downstream Gaussian-channel description for the GG02 protocol, whereas transmitted-reference architectures incur an extra protocol-dependent reference-noise penalty arising from signal-pilot phase mismatch and loss of post-coupling coherence; the signal coupling law alone is therefore insufficient in the pilot-assisted case.

What carries the argument

The scalar effective law for SMF coupling efficiency, obtained by projecting the collected field onto the guided fiber mode after finite-aperture collection.

If this is right

  • Mean-loss models alone overestimate key rates for GG02 under turbulence.
  • Pilot-assisted protocols must track an additional differential reference observable beyond the signal coupling statistics.
  • The effective model remains Gaussian for GG02 once the scalar coupling law is applied.
  • Signal and pilot turbulence realizations remain correlated yet non-identical, producing measurable phase mismatch after fiber projection.

Where Pith is reading between the lines

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

  • Receiver designs could adaptively switch between scalar-coupling and full-differential tracking depending on the chosen protocol.
  • The same phase-screen framework might be reused to test whether adaptive optics at the receiver can reduce the extra reference noise in pilot-assisted cases.
  • Experimental campaigns could measure the correlation length between signal and pilot coupling efficiencies to bound the size of the additional noise term.

Load-bearing premise

The turbulence can be represented by split-step propagation through random phase screens in which the signal and pilot experience correlated but non-identical realizations generated by a frozen-flow construction.

What would settle it

Numerical comparison of key rates computed from the scalar coupling law against full end-to-end simulation of the GG02 protocol under the same phase-screen realizations would show systematic deviation if the scalar law is inadequate.

Figures

Figures reproduced from arXiv: 2606.24431 by Arnaud Coatanhay, Hesham S. Ibrahim.

Figure 1
Figure 1. Figure 1: FIG. 1. Comparison between the full optical model, a mean [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Comparison between the scalar GG02 baseline [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: The scalar baseline remains stable because it [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Delay scan at [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Delay dependence of the effective key rate. The scalar [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Supplementary pilot-assisted diagnostic showing the [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Comparison between the full optical model and fac [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Supplementary coherence-based delay diagnostic. [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Representative convergence diagnostics for the Monte [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
read the original abstract

We study free-space continuous-variable quantum key distribution (CV-QKD) with single-mode fiber (SMF) reception under atmospheric turbulence. The optical channel is modeled by split-step propagation through random phase screens, followed by finite-aperture collection and projection onto the guided receiving mode. We first examine the standard GG02 setting and ask which receiver-side observable is sufficient for effective key-rate prediction. We show that a mean-loss description is generally too optimistic, whereas a scalar effective law for the SMF coupling efficiency provides an accurate downstream Gaussian-channel description within the effective model considered here. We then extend the optical model to a pilot-assisted architecture in which the signal and pilot propagate through correlated but non-identical turbulent realizations generated by a frozen-flow construction. In this case, the signal coupling law alone is no longer sufficient: signal--pilot phase mismatch and loss of post-coupling coherence produce an additional protocol-dependent reference-noise penalty. The results distinguish two regimes: a scalar coupling description is largely adequate for GG02, while transmitted-reference architectures require an additional differential reference observable beyond the signal coupling statistics.

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 / 2 minor

Summary. The paper models free-space CV-QKD with SMF reception via split-step propagation through random phase screens, finite-aperture collection, and projection onto the guided mode. For the GG02 protocol it shows that a mean-loss description is too optimistic while a scalar effective law for SMF coupling efficiency yields an accurate downstream Gaussian-channel description; for pilot-assisted architectures using frozen-flow correlated but non-identical turbulence realizations, signal-pilot phase mismatch and post-coupling coherence loss produce an additional protocol-dependent reference-noise penalty, so that the signal coupling law alone is insufficient and a differential reference observable is required.

Significance. If the numerical results hold within the stated effective model, the work supplies concrete guidance on which receiver-side observables suffice for key-rate prediction in turbulent free-space CV-QKD, cleanly separating the GG02 case from transmitted-reference architectures. The use of a frozen-flow construction to generate correlated turbulence realizations is a reproducible modeling choice that strengthens the comparison between protocols.

minor comments (2)
  1. [Abstract] Abstract: the phrase 'within the effective model considered here' is appropriately scoped but would benefit from an explicit forward reference to the section that defines the split-step parameters and frozen-flow construction.
  2. The manuscript would be improved by a short table (perhaps in §4 or §5) that tabulates the effective coupling law parameters, the resulting excess noise values, and the key-rate impact for both GG02 and pilot-assisted cases under identical turbulence realizations.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and accurate summary of our manuscript, the recognition of its significance, and the recommendation for minor revision. No major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central claims rest on numerical simulations of the optical channel (split-step phase screens, finite-aperture collection, projection onto SMF mode, and frozen-flow correlated turbulence realizations) to compare mean-loss, scalar coupling efficiency, and full statistics for GG02 key rates, plus the need for an extra differential observable in pilot-assisted cases. These are direct empirical comparisons inside the stated model rather than derivations that reduce to fitted parameters or self-citations by construction. No equations or load-bearing steps in the provided text exhibit self-definition, renaming of known results, or uniqueness imported from prior author work; the results are scoped explicitly to the simulation framework and therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only; no free parameters, axioms, or invented entities identifiable. Full text required to audit modeling assumptions such as phase screen statistics or frozen-flow parameters.

pith-pipeline@v0.9.1-grok · 5725 in / 1048 out tokens · 26087 ms · 2026-06-26T00:00:43.667685+00:00 · methodology

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Reference graph

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