Security Analysis of MDI-QKD in Turbulent Free-Space Polarization Channels-A Composite Channel Framework

Heyang Peng; Seid Koudia; Symeon Chatzinotas

REVIEW 3 major objections 4 minor 1 cited by

Security Analysis of MDI-QKD in Turbulent Free-Space Polarization Channels-A Composite Channel Framework

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper claims that atmospheric turbulence can be reduced to three closed-form parameters that plug directly into an analytic secret-key-rate formula for free-space MDI-QKD.

desk verdict The composite-channel idea is genuinely useful, but the depolarization formula is internally inconsistent with the paper's own axis-averaging derivation, and the abstract overclaims validation. read the letter →

arxiv 2509.02087 v1 pith:2KZV6WRP submitted 2025-09-02 quant-ph

Heyang Peng , Seid Koudia , Symeon Chatzinotas This is my paper

classification quant-ph MSC 81P94 PACS 03.67.Dd

keywords measurement-device-independentQKDfree-spaceopticalquantumcommunicationatmosphericturbulencepolarizationdecoherencedepolarizing–dephasingchannelsecretkeyrateSU(2)rotationground-to-satellitelink

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Atmospheric turbulence scrambles the polarization of photons and, in free-space measurement-device-independent QKD, that scrambling eats into the secret key rate. This paper claims that all the relevant impairments—phase perturbations, beam spreading, beam drift, aperture truncation, and scintillation—can be consolidated into three closed-form channel parameters: a depolarization factor, a decoherence factor, and a detection probability. Given those three numbers, the secret key rate is an explicit analytic formula, so link design and real-time adaptation no longer require heavy wave-optics simulations. The argument works by treating turbulence as random SU(2) polarization rotations whose axes are von Mises–Fisher/Watson distributed and whose angle variance is set by the phase structure function. If the mapping is right, the same three-parameter interface applies to clear, overcast, and hazy uplinks and to both link directions.

What carries the argument

The mechanism is a sequence of four channels, E_composite = E_aperture ∘ E_drift ∘ E_spread ∘ E_phase. The phase channel is the one that touches polarization: each transverse point applies a random SU(2) rotation U(θ, n) = cos(θ/2)I − i sin(θ/2)(n·σ), where the rotation angle θ is Gaussian with variance set by the phase structure function D_φ(r) = 1.09 k² z ⟨C_n²⟩ r^{5/3}, and the axis n is drawn from a von Mises–Fisher/Watson distribution with concentration κ around the propagation direction. Averaging over θ and n converts each point's state into the depolarizing–dephasing form with local factors λ(r) and r̄²(r, κ). The spread, drift, and aperture steps then spatially average these factors

What would settle it

Send a linearly polarized Gaussian beam through a turbulence cell with known path-averaged C_n² in the weak Rytov regime (σ_R² < 1) and measure the depolarization factor from Stokes parameters. In the small-angle limit the paper's model predicts a slope of D_φ/4, while standard isotropic rotation averaging gives D_φ/3; observing D_φ/3, or any mismatch not explained by aperture averaging, would falsify the quantitative key-rate predictions.

Watch

Extended reading notes

Core claim

The paper claims that, in the weak-turbulence regime (Rytov variance σ_R² ≤ 1), the full set of atmospheric impairments can be replaced by three closed-form parameters—depolarization factor λ_a^eff, decoherence factor r_{2,a}^eff, and detection probability η_eff—which enter directly into the analytic MDI-QKD secret-key-rate expression R = η_A η_B [(2 − λ_A − λ_B + λ_A λ_B)(1 − H((1 − (1 − λ_A)(1 − λ_B) r̄⁴)/2)) − (1/2) f H((λ_A + λ_B − λ_A λ_B)/2)]. It further claims that this composite depolarizing–dephasing channel remains accurate under clear, overcast, and hazy Hufnagel–Valley profiles and reproduces expected ground-to-satellite uplink behavior: turbulence dominates near the ground, then

Load-bearing premise

The load-bearing premise is that turbulence-induced wavefront phase fluctuations act like an effective birefringence, so the amount of polarization rotation is set by the same variance that describes scalar phase fluctuations; the paper asserts this phase-to-rotation link rather than deriving it from the equations of light propagation, and if the link is wrong by a constant factor, every predicted key rate shifts.

Editorial extensions

If this is right

With λ_a^eff, r_{2,a}^eff, and η_eff in hand, the secret key rate becomes a closed-form function of distance, aperture, weather, and adaptive-optics strength, enabling rapid parameter sweeps without wave-optics simulations.
Larger receiver apertures improve key rate and range by collecting more light and averaging over turbulence-induced phase perturbations.
Adaptive optics extends the usable link range in the paper's simulations—for example, to about 100 km in clear and 50 km in overcast conditions at a 0.7 m aperture.
Scintillation affects only the detection probability, not the polarization state, so the depolarization and decoherence parameters can be characterized independently of intensity fading.
The same three-parameter interface can feed directly into the existing decoy-state MDI-QKD security analysis, giving a plug-compatible turbulence model for security proofs.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The three-parameter interface is protocol-agnostic on the polarization side; the same λ_a^eff, r_{2,a}^eff, and η_eff could be substituted into other polarization-encoded QKD protocols, such as BB84 or entanglement-based schemes, without redoing the turbulence modelling.
Because scintillation provably cancels out of the normalized polarization state, a tabletop turbulence chamber with polarimetric detection could calibrate κ(σ_R²) and test the phase-to-rotation relation before any satellite deployment.
The paper's most consequential quantitative assumption is the small-angle coefficient linking depolarization to the phase structure function; testing that coefficient against independent averaging calculations is a cheaper and more decisive check than extending the model to strong turbulence.
The model is memoryless in its parameters, so temporal correlations and adaptive-optics closed-loop lag are not captured; a time-series extension would be needed before relying on the formula for rapidly varying turbulence.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The genuinely new thing here is consolidating turbulence impairments into a closed-form depolarizing-dephasing channel for MDI-QKD by averaging SU(2) rotations with a Fisher–Watson axis distribution. The resulting SKR expression is clean and computationally cheap, and it connects turbulence physics to existing MDI-QKD security analyses. That is a real contribution, and the authors are unusually explicit about assumptions and limitations. But there is a load-bearing math slip you should know about before trusting any number.

In the isotropic-axis limit κ=0, their own Eq. (78) gives a depolarization factor λ = (2/3)(1−cosθ), which after Gaussian averaging is Dϕ/3 for small Dϕ. Eq. (38) instead gives λ = (1−e^{−Dϕ/2})/2 ≈ Dϕ/4. That is a factor-4/3 discrepancy. The same inconsistency appears in the decoherence factor: for κ=0 their Eq. (39) forces r̄²=1, but direct averaging of Eq. (78) shows off-diagonal damping proportional to (2/3)sin²(θ/2), which is not captured. Since λ and r̄² enter QBER and SKR multiplicatively, all quantitative SKR curves in Section IV inherit this error unless κ is treated as a fitting parameter. κ is already phenomenological, so calibration could mask the slip, but then the closed-form, parameter-free selling point weakens.

I also have a smaller but important complaint about the validation claim. The abstract says numerical simulations "confirm its accuracy," but the paper itself states that no head-to-head benchmark against wave-optics Monte Carlo is included and that quantifying model bias is left for future work. The simulations are self-consistency checks, not validation. That overstatement should be fixed. The phase-to-SU(2)-rotation mapping is also asserted rather than derived; the effective-birefringence argument is plausible but not tested. So the framework is promising, but the quantitative predictions are not yet trustworthy.

The paper is for people working on satellite-QKD link design and MDI-QKD security analysis who want fast estimates. With the factor fixed and a wave-optics benchmark, it would be a solid paper. As it stands, I would not cite the numbers. But I would send it to review: the bug is localized, the machinery is worth a careful referee pass, and the authors show honest engagement with the literature.

Referee Report

3 major / 4 minor

Summary. The paper proposes a composite quantum channel model for polarization-encoded free-space MDI-QKD under atmospheric turbulence. It maps turbulence-induced wavefront phase perturbations to random SU(2) polarization rotations, with rotation axes drawn from a von Mises-Fisher/Watson distribution and rotation angles Gaussian with variance equal to the phase structure function D_phi(r). Spatial averaging over Gaussian beam spreading, beam drift, aperture truncation, and scintillation yields three effective closed-form parameters (depolarization factor lambda_eff, decoherence factor r2_eff, detection probability eta_eff), which are inserted into a Devetak-Winter secret-key-rate expression. Numerical simulations for ground-to-satellite uplinks under clear, overcast, and hazy weather and various AO profiles are presented as evidence of the model's accuracy.

Significance. If the model and its derivations were correct, the framework would be useful: it offers a computationally light, closed-form description of turbulence effects on polarization qubits that could support real-time link adaptation and integrate directly with existing MDI-QKD security analyses. However, the current manuscript contains a mathematically load-bearing error in the depolarization-factor derivation, and the claimed numerical validation is not supported by any benchmark against wave-optics or polarimetric data. The central quantitative predictions are therefore not reliable as they stand.

major comments (3)

[Section II-H.1, Eq. (38); Appendix B, Eq. (78)] The depolarization factor is inconsistent with the paper's own SU(2) rotation model. For an isotropic axis distribution (kappa=0), rotational covariance requires the averaged channel to be an isotropic depolarizing channel with Bloch shrinkage (1+2<cos theta>)/3, giving lambda=(1-exp(-D_phi/2))/3 for Gaussian theta. Eq. (38) instead gives (1-exp(-D_phi/2))/2, a factor 4/3 discrepancy at small D_phi. The source is Eq. (78), which for kappa=0 produces different Bloch shrinkages for x/y and z (z is unaffected), violating rotational covariance. Eq. (39) also gives nonzero lambda in the kappa->infinity aligned limit, where pure dephasing requires lambda=0. Since lambda enters QBER (Eq. 59) and SKR (Eq. 62) multiplicatively, all quantitative SKR values in Section IV are affected.
[Section IV and Section V] The abstract and Section IV state that numerical simulations 'confirm its accuracy,' but Section V explicitly says: 'We do not include a head-to-head benchmark against wave-optics Monte Carlo; quantifying model bias relative to phase-screen simulations is left for future work.' The figures in Section IV are self-consistency evaluations under the model's own parameters, not validation against wave optics or polarimetric measurements. Moreover, the parameters kappa and alpha are acknowledged as phenomenological, with calibration left to future work. The claim of numerical confirmation is therefore unsupported.
[Section II-B and II-H.1, Eq. (37)] The mapping from wavefront phase fluctuations to SU(2) polarization rotations is a non-derived modeling assumption. The paper asserts that 'phase gradients can act as an effective birefringence' and sets the rotation-angle variance equal to D_phi(r), but this is not derived from Maxwell/Stokes equations and is not tested against wave-optics or polarimetry. If this mapping is off by a constant factor, all SKR predictions scale accordingly. At minimum, this should be framed as a phenomenological ansatz with a sensitivity analysis or a concrete validation plan, not as a physically established relation.

minor comments (4)

[Eq. (7) and Eq. (8)] The axis distribution w_kappa(vartheta) already contains a factor sin(vartheta), but Eq. (8) multiplies by another sin(vartheta), so the joint density is not normalized. This likely contributes to the incorrect isotropic average in Appendix B.
[Appendix D] The sentence 'where eta(r), lambda_a(r), r2_a(r) are defined in the main text, and where eta(r), lambda_a(r), r2_a(r) are defined in the main text' is duplicated and should be corrected.
[Eq. (31)] Typo: 'vaccum' should be 'vacuum'.
[Fig. 8 caption] Minor typo: 'hazey' should be 'hazy'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the analytic SKR follows from standard MDI-QKD formulas into which independently derived turbulence parameters are inserted; the acknowledged phenomenological constants are calibrated outside SKR, and the self-citation is not load-bearing.

full rationale

The paper's derivation chain is: (i) model turbulence as random SU(2) rotations with Fisher–Watson-distributed axes; (ii) derive local depolarization λ(r) and decoherence r̄²(r,κ) by averaging; (iii) spatially average over Gaussian beam, drift, and aperture to obtain λ_a^eff, r2_a^eff, η_eff; (iv) insert these into the MDI-QKD secret-key-rate formula. I checked for circular reductions. The SKR formula (62) is quoted from [38], which shares authors with this paper, but it is the standard Devetak–Winter form for MDI-QKD decoy states (Eqs. 57–62 and Appendix E); the turbulence parameters enter only as multiplicative factors and the formula does not encode the turbulence model, so the self-citation is not load-bearing. The concentration parameter κ and medium-turbulence interpolant α are explicitly acknowledged as phenomenological ('Our use of κ is phenomenological... a practical calibration κ(σ_R²) may be obtained by fitting least squares to wave optic data sets or on-sky polarimetry'; 'The mixing parameter α = 1−σ_R²/5 is a phenomenological interpolant'), and calibration is suggested against wave-optics/polarimetry data, not against SKR. Hence the SKR is a model consequence, not a fit to itself. No equation is defined in terms of the target quantity. There is an internal inconsistency: Eq. (38) gives λ ≈ D_φ/4 in the isotropic limit, whereas averaging the paper's own SU(2) formula in Appendix B for κ=0 gives λ ≈ D_φ/3. That is a mathematical/physics error, not circularity. The paper also explicitly disclaims a head-to-head benchmark against wave-optics Monte Carlo, further confirming that its 'validation' is not an independent test but this is a limitation, not a circular reduction.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

No new physical entities are introduced. The free parameters are the phenomenological concentration kappa, the medium-turbulence interpolant alpha, the AO scaling profiles, and the site-dependent weather mapping. The axioms cover the unverified phase-to-rotation mapping, the Gaussian angle distribution, the polarization-insensitive/scintillation-cancellation approximations, and the use of the authors' own security analysis [38] as a black box.

free parameters (4)

kappa (axis concentration) = not specified
Phenomenological; Section II-H states a practical calibration kappa(sigma_R^2) may be obtained by fitting to wave optic data sets or on-sky polarimetry. It controls r2_a^eff through mu_parallel(kappa).
alpha (medium turbulence interpolant) = alpha = 1 - sigma_R^2/5
Section II-H.2: 'a phenomenological interpolant that enforces continuity between the weak-law and a Haar-averaged limit. It should be regarded as a conservative surrogate rather than a unique physical law.'
AO scaling parameters (rho_trk, kappa_w, kappa_phi) = three profiles in Table I
Adaptive-optics profiles are parametric scaling choices; the paper says the AO model 'does not include closed-loop bandwidth or temporal lag' and 'is parametric'.
Weather HV parameters (A, v, alpha_atm) = clear/overcast/hazy sets in Table I
The paper admits 'the HV parameters (A, v) and alpha_atm are site- and season-dependent; our weather mapping is a representative but not universal choice.'

assumptions (6)

ad hoc to paper Wavefront phase gradients act as effective birefringence producing random SU(2) polarization rotations
Section II states this as the physical motivation ('these phase gradients can act as an effective birefringence... resulting in random SU(2) rotations'), but it is not derived from electromagnetic propagation or Maxwell equations.
ad hoc to paper The rotation angle theta is Gaussian with variance D_phi(r)
Eq. (37) sets p(theta | r) = exp(-theta^2 / (2 D_phi(r))) / sqrt(2 pi D_phi(r)) with D_phi the phase structure function. This is asserted without a derivation from the phase structure function.
domain assumption Polarization-insensitive receiver and no diattenuation in the optical train
Section II-A assumes a nonpolarizing receiver and neglects aerosol/coating diattenuation at first order in the weak-turbulence regime.
domain assumption Scintillation cancels in the normalized polarization state
Appendix D shows I0 cancels in normalization under the assumptions of polarization-insensitive coupling, linear detector response, and no polarization-dependent loss. This is an approximation that the paper itself flags.
domain assumption The security analysis equations of [38] (thermal-loss and phase-noise MDI-QKD) are valid and applicable here
The QZ, Q11, EZ, and eXX expressions (Eqs. 57-60) are taken directly from the authors' prior conference paper [38] without derivation or independent verification.
domain assumption Weak turbulence regime sigma_R^2 <= 1 for all quantitative claims
Section II explicitly scopes all derivations and quantitative claims to the weak-turbulence regime; medium and strong forms are included only for completeness.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Security Analysis of MDI-QKD in Turbulent Free-Space Polarization Channels-A Composite Channel Framework." pith.science (2026). https://pith.science/paper/2KZV6WRP

@misc{pith2026250902087,
  author       = {Pith},
  title        = {Pith review of: Security Analysis of MDI-QKD in Turbulent Free-Space Polarization Channels-A Composite Channel Framework},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2KZV6WRP}},
  note         = {Machine review of arXiv:2509.02087}
}

read the original abstract

Atmospheric turbulence poses a significant challenge to free-space measurement-device-independent quantum key distribution (FSO MDI-QKD) by inducing polarization decoherence and depolarization, which degrade the secret key rate (SKR). In this paper, we propose a unified depolarizing-dephasing channel model for turbulence-induced polarization decoherence in FSO MDI-QKD. This model consolidates phase perturbations, Gaussian beam spreading, beam drift, aperture truncation, and scintillation into closed-form parameters: depolarization factor, decoherence factor, and detection probability. By mapping turbulence to a von Mises-Fisher/Watson-distributed SU(2) rotation, we derive an analytic SKR expression compatible with existing MDI-QKD security analyses. The model excels in clear, overcast, and hazy weather conditions, offering computational efficiency and experimental verifiability for real-time link adaptation. Numerical simulations, illustrated on a ground-to-satellite free-space link, confirm its accuracy, enabling robust physical layer design for global-scale MDI-QKD networks.

Figures

Figures reproduced from arXiv: 2509.02087 by the authors.

**Figure 2.** Illustration of turbulence-induced polarization rotation on the Bloch [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Illustration of beam spreading and beam drift in turbulent free-space [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Uplink SKR versus transmission distance, combining aperture/turbulence sweeps and elevation dependence. Panels (a)–(c): full range (0–200 km) [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: Uplink depolarization coefficient λ (top row) and decoherence coefficient r 2 (bottom row) versus transmission distance and receiver aperture radius, with adaptive optics (AO). Range: 0–200 km. (a),(d) Clear; (b),(e) Overcast; (c),(f) Hazy. Axes: horizontal—distance (k…

**Figure 7.** Figure 7: Effect of AO strength on uplink SKR (clear turbulence, [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

**Figure 8.** Figure 8: Uplink decoy-state MDI-QKD SKR vs distance (a) clear/overcast/haze [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Continuous Noise Model for Quantum Circuits
quant-ph 2026-04 unverdicted novelty 6.0 of 10

On small stabilizer-code and Grover circuits, coherent Gaussian noise and Pauli noise rank differently under entropy-matched comparison, and a simplified variance-propagation model matches full simulation only in unco...

Reference graph

Works this paper leans on

39 extracted references · 37 canonical work pages · cited by 1 Pith paper

[1]

Quantum cryptography: Public key distribution and coin tossing,

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proc. IEEE Int. Conf. Comput., Syst. Signal Process., Bangalore, India, 1984, pp. 175–179

work page 1984
[2]

Quantum cryptography based on Bell’s theorem,

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett., vol. 67, no. 6, pp. 661–663, Aug. 1991

work page 1991
[3]

Measurement-device-independent quantum key distribution,

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. , vol. 108, no. 13, p. 130503, Mar. 2012

work page 2012
[4]

Side-channel-free quantum key distribution,

S. L. Braunstein and S. Pirandola, “Side-channel-free quantum key distribution,” Phys. Rev. Lett. , vol. 108, no. 13, p. 130502, Mar. 2012

work page 2012
[5]

Advances in quantum teleportation,

S. Pirandola et al. , “Advances in quantum teleportation,” Nat. Photon. , vol. 9, no. 10, pp. 641–652, Oct. 2015

work page 2015
[6]

Satellite-based entanglement distribution over 1200 km,

J. Yin et al. , “Satellite-based entanglement distribution over 1200 km,” Science, vol. 356, no. 6343, pp. 1140–1144, Jun. 2017

work page 2017
[7]

A comprehensive design and performance analysis of low Earth orbit satellite quantum communication,

J.-P. Bourgoin et al., “A comprehensive design and performance analysis of low Earth orbit satellite quantum communication,” New J. Phys. , vol. 15, no. 2, p. 023006, Feb. 2013

work page 2013
[8]

Analysis of satellite-to-ground quantum key distribution with adaptive optics,

V . Marulanda Acosta et al. , “Analysis of satellite-to-ground quantum key distribution with adaptive optics,” New J. Phys. , vol. 26, no. 4, p. 043034, Feb. 2024

work page 2024

Show all 39 references

[9]

Long-distance free-space measurement-device- independent quantum key distribution,

Y . Cao et al. , “Long-distance free-space measurement-device- independent quantum key distribution,” Phys. Rev. Lett. , vol. 125, no. 26, p. 260503, Dec. 2020

2020
[10]

Quantum repeaters in space,

C. Liorni, H. Kampermann, and D. Bruß, “Quantum repeaters in space,” New J. Phys. , vol. 23, no. 5, p. 053021, May 2021

2021
[11]

Advances in space quantum communications,

J. S. Sidhu et al. , “Advances in space quantum communications,” IET Quantum Commun. , vol. 2, no. 4, pp. 182–217, Dec. 2021

2021
[12]

Quantum repeaters: From quantum networks to the quantum internet,

K. Azuma et al. , “Quantum repeaters: From quantum networks to the quantum internet,” Rev. Mod. Phys. , vol. 95, no. 4, p. 045006, Dec. 2023

2023
[13]

Atmospheric turbulence effects on an OAM-multiplexed FSO link,

Y . Ren et al. , “Atmospheric turbulence effects on an OAM-multiplexed FSO link,” Opt. Lett. , vol. 38, no. 20, pp. 4062–4065, Oct. 2013

2013
[14]

Advances in communications using optical vortices,

J. Wang, “Advances in communications using optical vortices,” Photon. Res., vol. 4, no. 5, pp. B14–B28, Oct. 2016

2016
[15]

Atmospheric quantum channels with weak and strong turbulence,

D. Vasylyev, A. A. Semenov, and W. V ogel, “Atmospheric quantum channels with weak and strong turbulence,” Phys. Rev. Lett. , vol. 117, no. 9, p. 090501, Aug. 2016

2016
[16]

Free-space quantum links under diverse weather conditions,

D. Vasylyev, A. A. Semenov, and W. V ogel, “Free-space quantum links under diverse weather conditions,” Phys. Rev. A , vol. 96, no. 4, p. 043856, Oct. 2017

2017
[17]

Characterization of free- space quantum channels,

D. Vasylyev, A. A. Semenov, and W. V ogel, “Characterization of free- space quantum channels,” in Proc. SPIE, vol. 10771, p. 107710V , Sep. 2018

2018
[18]

Polarization measurements through space-to- ground atmospheric propagation paths by using a highly polarized laser source in space,

M. Toyoshima et al. , “Polarization measurements through space-to- ground atmospheric propagation paths by using a highly polarized laser source in space,” Opt. Express, vol. 17, no. 25, pp. 22333–22340, Dec. 2009

2009
[19]

Quantum communications in a moderate- to-strong turbulent space,

M. Ghalaii and S. Pirandola, “Quantum communications in a moderate- to-strong turbulent space,” Commun. Phys. , vol. 5, no. 1, p. 38, Feb. 2022

2022
[20]

High-speed free-space optical continuous variable quantum key distribution enabled by three-dimensional multi- plexing,

Z. Qu and I. B. Djordjevic, “High-speed free-space optical continuous variable quantum key distribution enabled by three-dimensional multi- plexing,” Opt. Express, vol. 24, no. 26, pp. 29149–29159, Dec. 2016

2016
[21]

Influence of turbulence on OAM communications,

M. Malik et al. , “Influence of turbulence on OAM communications,” Opt. Express, vol. 20, no. 12, pp. 13195–13200, Jun. 2012

2012
[22]

Changes in the polarization ellipse of random beams in turbulence,

O. Korotkova et al. , “Changes in the polarization ellipse of random beams in turbulence,” Waves Random Complex Media , vol. 15, no. 3, pp. 353–369, Oct. 2005

2005
[23]

QBER estimation in QKD systems with polarization encoding,

N. J. Muga, M. F. S. Ferreira, and A. N. Pinto, “QBER estimation in QKD systems with polarization encoding,” J. Lightw. Technol., vol. 29, no. 3, pp. 355–361, Feb. 2011

2011
[24]

Turbulence mitigation in an OAM FSO link with adaptive optics,

Y . Ren et al., “Turbulence mitigation in an OAM FSO link with adaptive optics,” Opt. Lett. , vol. 41, no. 11, pp. 2406–2409, Jun. 2016

2016
[25]

Approaching Gb/s secret-key rates in an FSO CV-QKD system affected by atmospheric turbulence,

Z. Qu and I. B. Djordjevic, “Approaching Gb/s secret-key rates in an FSO CV-QKD system affected by atmospheric turbulence,” inProc. 43rd Eur . Conf. Opt. Commun. (ECOC) , Gothenburg, Sweden, Sep. 2017

2017
[26]

Adaptive-optics mitigation for OAM-QKD in turbulence,

Z. Tao et al., “Adaptive-optics mitigation for OAM-QKD in turbulence,” Opt. Express, vol. 29, no. 20, pp. 31078–31092, Sep. 2021

2021
[28]

Beam propagation through atmospheric turbulence using the split-step method,

Y . K. Chahine et al., “Beam propagation through atmospheric turbulence using the split-step method,” NASA, Tech. Rep. NTRS 20200001115, Feb. 2020

2020
[29]

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media , 2nd ed. Bellingham, W A, USA: SPIE Press, 2005

2005
[30]

Physical layer aspects of quantum communications: A survey,

S. Koudia et al. , “Physical layer aspects of quantum communications: A survey,” arXiv:2407.09244 [quant-ph], Jul. 2024. [Online]. Available: https://arxiv.org/abs/2407.09244

2024 arXiv
[31]

Spatial-mode diversity and multiplexing for continuous-variable quantum communications,

S. Koudia et al. , “Spatial-mode diversity and multiplexing for continuous-variable quantum communications,” arXiv:2409.04334 [quant-ph], Sep. 2024. [Online]. Available: https://arxiv.org/abs/2409. 04334

2024 arXiv
[32]

Diversity and multiplexing in quantum MIMO channels,

J. ur Rehman et al. , “Diversity and multiplexing in quantum MIMO channels,” EPJ Quantum Technol. , vol. 12, p. 18, Feb. 2025

2025
[33]

Continuous-variable MDI QKD in free- space channels,

M. Ghalaii and S. Pirandola, “Continuous-variable MDI QKD in free- space channels,” Phys. Rev. A , vol. 108, no. 4, p. 042621, Oct. 2023

2023
[34]

Entanglement-based QKD in the daylight and uplink satellite configuration: Proof-of-principle and feasibility,

K. Joarder, J. Szlachetka, and P. Kolenderski, “Entanglement-based QKD in the daylight and uplink satellite configuration: Proof-of-principle and feasibility,” arXiv:2501.17130 [quant-ph] , Jan. 2025. [Online]. Available: https://arxiv.org/abs/2501.17130

2025 arXiv
[35]

Daylight entanglement-based QKD with a quantum-dot source,

F. Basso Basset et al. , “Daylight entanglement-based QKD with a quantum-dot source,” Quantum Sci. Technol. , vol. 8, no. 2, p. 025002, Apr. 2023

2023
[36]

Performance analysis of OOK-based FSO systems in Gamma–Gamma turbulence with imprecise channel models,

J. Feng, G. Wei, and J. Li, “Performance analysis of OOK-based FSO systems in Gamma–Gamma turbulence with imprecise channel models,” Opt. Commun. , vol. 402, pp. 340–346, Nov. 2017

2017
[37]

Statistical verifications and deep-learning predictions for satellite-to-ground quantum atmospheric channels,

P. V . Trinh et al., “Statistical verifications and deep-learning predictions for satellite-to-ground quantum atmospheric channels,” Commun. Phys., vol. 5, no. 1, p. 225, Sep. 2022

2022
[38]

Performance analysis of MDI-QKD in thermal-loss and phase-noise channels,

H. Peng et al., “Performance analysis of MDI-QKD in thermal-loss and phase-noise channels,” in Proc. IEEE Int. Conf. Quantum Comput. Eng. (QCE), Aug. 2025. [Online]. Available: https://arxiv.org/abs/2504.16561

2025 arXiv
[39]

Satellite-to-ground quantum key distribution,

S.-K. Liao et al., “Satellite-to-ground quantum key distribution,” Nature, vol. 549, pp. 43–47, Sep. 2017

2017
[40]

Satellite-relayed intercontinental quantum network,

S.-K. Liao et al. , “Satellite-relayed intercontinental quantum network,” Phys. Rev. Lett. , vol. 120, no. 3, p. 030501, Jan. 2018

2018

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [1]

Quantum cryptography: Public key distribution and coin tossing,

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” in Proc. IEEE Int. Conf. Comput., Syst. Signal Process., Bangalore, India, 1984, pp. 175–179

work page 1984

[2] [2]

Quantum cryptography based on Bell’s theorem,

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett., vol. 67, no. 6, pp. 661–663, Aug. 1991

work page 1991

[3] [3]

Measurement-device-independent quantum key distribution,

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. , vol. 108, no. 13, p. 130503, Mar. 2012

work page 2012

[4] [4]

Side-channel-free quantum key distribution,

S. L. Braunstein and S. Pirandola, “Side-channel-free quantum key distribution,” Phys. Rev. Lett. , vol. 108, no. 13, p. 130502, Mar. 2012

work page 2012

[5] [5]

Advances in quantum teleportation,

S. Pirandola et al. , “Advances in quantum teleportation,” Nat. Photon. , vol. 9, no. 10, pp. 641–652, Oct. 2015

work page 2015

[6] [6]

Satellite-based entanglement distribution over 1200 km,

J. Yin et al. , “Satellite-based entanglement distribution over 1200 km,” Science, vol. 356, no. 6343, pp. 1140–1144, Jun. 2017

work page 2017

[7] [7]

A comprehensive design and performance analysis of low Earth orbit satellite quantum communication,

J.-P. Bourgoin et al., “A comprehensive design and performance analysis of low Earth orbit satellite quantum communication,” New J. Phys. , vol. 15, no. 2, p. 023006, Feb. 2013

work page 2013

[8] [8]

Analysis of satellite-to-ground quantum key distribution with adaptive optics,

V . Marulanda Acosta et al. , “Analysis of satellite-to-ground quantum key distribution with adaptive optics,” New J. Phys. , vol. 26, no. 4, p. 043034, Feb. 2024

work page 2024