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REVIEW 4 major objections 5 minor 35 references

Robustness of WDM technique for the co-propagation of quantum with classical signals in an optical fiber

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Two ITU channels of separation make WDM crosstalk negligible

desk verdict The positive-P simulation of WDM co-propagation is new and the qualitative crosstalk trend is plausible, but the '2 ITU channels is sufficient' conclusion rests on an RMS-width metric that is blind to the phase distortions QKD actually suffers. read the letter →

arxiv 2411.16942 v2 pith:3XIDULIH submitted 2024-11-25 quant-ph

Sumit Chaudhary , Shahram Dehdashti , Igor Litvin , Janis Nötzel This is my paper · ORCID
classification quant-ph
keywords quantumkeydistributionwavelengthdivisionmultiplexingcrosstalknonlinearSchrödingerequationpositive-Prepresentationweakcoherentpulsesopticalfiberpropagationquantum-classicalcoexistence
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

The paper tries to establish that wavelength division multiplexing can carry weak quantum signals alongside strong classical data traffic in the same optical fiber with only a small wavelength guard band. It does this with a quantum-mechanical model of pulse propagation based on the positive-P representation of the nonlinear Schrödinger equation, in which the classical channel is a 16-QAM signal and the quantum channel a weak coherent pulse. The model finds that crosstalk is noticeable only for the two nearest ITU channels, and that separating the signals by two ITU channels, about 2.39 nm on the 100 GHz grid, gives essentially the same quantum pulse as dark fiber. If this is right, QKD systems could be integrated into standard telecom infrastructure rather than requiring dedicated dark fibers.

What carries the argument

The central object is the positive-P representation of the generalized nonlinear Schrödinger equation, which converts the quantum evolution of a field in a lossy Kerr fiber into two coupled stochastic differential equations for scaled field variables $\phi(\zeta,\tau)$ and $\phi^+(\zeta,\tau)$. Crosstalk is quantified by $C(\zeta)$, the ratio of the root-mean-square temporal width of the quantum pulse recovered from its ITU channel after spectral filtering to the width the same pulse would have in dark fiber. The stochastic equations are integrated with the Ito semi-implicit midpoint split-step method, with a 16-QAM classical signal at 10 Gbps as the interfering field.

What would settle it

Run the same model with a quantum bit error rate or phase-quadrature variance as the output metric instead of $C(\zeta)$ for a two-channel separation at 1 mW to 10 mW classical launch power; if the QBER stays above the protocol's error threshold while $C(\zeta)\approx 1$, the two-channel separation claim fails.

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Extended reading notes

Core claim

The central claim is that the crosstalk between a weak quantum pulse and a strong classical signal co-propagating over 50 km of standard single-mode fiber depends mainly on the wavelength separation and the classical launch power. With the quantum signal fixed in ITU channel 38 and the classical channel varied across the C-band, only the adjacent and next-nearest channels raise the crosstalk metric $C(\zeta)$ above 1, and the effect grows monotonically with launch power from 0.1 mW to 100 mW. For separations of two ITU channels or more, $C(\zeta)$ stays near 1, meaning the quantum pulse is as clean as if it had propagated alone. The authors conclude that two empty ITU channels, 2.39 nm, suffice for negligible crosstalk, and that shorter quantum pulses at fixed photon number reduce crosstalk, which would favour higher-clock-rate QKD.

Load-bearing premise

The central claim assumes that crosstalk is fully captured by the widening of the quantum pulse's root-mean-square temporal width, so a classical signal that adds phase noise, frequency jitter, or spectral contamination without broadening the envelope would be counted as harmless even if it degrades QKD.

Editorial extensions

If this is right

  • A separation of two ITU channels on the 100 GHz grid is sufficient for negligible crosstalk, so QKD and classical traffic can share one fiber.
  • Crosstalk rises monotonically with classical launch power for adjacent channels, so launch-power budgets must be set per channel rather than globally.
  • Narrowing the quantum pulse at constant photon number lowers crosstalk, implying that higher-repetition-rate QKD systems will coexist more easily with WDM traffic.
  • Channels beyond the two nearest neighbors can be treated as effectively isolated, simplifying power and wavelength planning in mixed quantum-classical links.

Reading between the lines

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

  • The ratio of RMS temporal widths captures broadening but not phase noise or frequency jitter, so phase-encoded QKD may show degradation even where $C(\zeta)\approx 1$; a calculation of the phase-error variance would settle this.
  • The paper's suspected 'sweet spot' in pulse duration is a concrete testable prediction: scanning $t_0$ at fixed channel spacing and photon number should show a minimum of crosstalk before subpicosecond Raman effects begin.
  • Adapting the formalism to Fock states would test whether single-photon sources behave differently from weak coherent pulses, since photon-number statistics change how nonlinear cross-phase modulation acts.
  • If the two-channel guard band holds in experiment, existing QKD deployments that use a full band separation, for example O-band versus C-band, may be wasting spectrum, and the guard band could be tightened.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This manuscript studies co-propagation of a weak quantum signal, modeled as a multimode coherent state with average photon number μ=0.4, together with a 16-QAM classical signal in standard single-mode fiber, using the positive-P representation of the generalized nonlinear Schrödinger equation with loss and Kerr noise. Crosstalk is quantified in Eq. (10) as the ratio C(ζ) of the RMS temporal width of the spectrally filtered quantum pulse in the presence of the classical signal to the corresponding width in dark fiber. Numerical simulations on a 100 GHz ITU grid in the C-band over a 50 km span show that C is close to 1 when the classical channel is separated from the quantum channel by two empty channels or more, and that C increases with classical launch power and with decreasing quantum pulse width. The paper concludes that a separation of 2 ITU channels is sufficient for negligible crosstalk and that the WDM technique is therefore robust for integrating QKD with classical traffic.

Significance. The question addressed is practically important: what guard band and launch-power constraints are needed for a QKD channel co-propagating with classical WDM traffic. A notable strength of the paper is that it starts from the established quantum GNLSE in the positive-P representation rather than from an ad hoc crosstalk model, and the input parameters are standard fiber and system values rather than parameters fitted to the output curves. If the central claim were fully supported, the result would simplify QKD deployment on existing fiber infrastructure. However, the central claim is currently tied to a pulse-width-ratio metric that is not linked to any QKD performance measure such as QBER or phase error; the authors themselves state in the Outlook that QBER should be used instead of C(ζ). The work is therefore a promising and potentially useful contribution, but the headline conclusion is not yet established.

major comments (4)
  1. [§III, Eq. (10), and §VI Conclusion] The conclusion that a separation of 2 ITU channels leads to negligible crosstalk is based entirely on the metric C(ζ), the ratio of RMS temporal widths of the filtered quantum pulse intensity. This metric is insensitive to phase and frequency perturbations: cross-phase modulation from the classical field imprints a time-dependent phase and frequency chirp on the weak quantum pulse, and phase-encoded or time-bin QKD can be degraded by such phase errors and timing jitter even when the RMS intensity envelope is unchanged. The spectral filter in Eq. (9) removes out-of-band classical power but not in-band phase distortion. The paper's own Outlook concedes that application-specific metrics like the quantum bit error rate are needed in place of C(ζ). The numerical results may be internally consistent, but they do not establish negligible crosstalk for QKD operation as claimed.
  2. [§IV, Fig. 2, and §VI Conclusion] There is an inconsistency between the headline 'separation of 2 ITU channels (2.39 nm)' and the standard 100 GHz ITU grid used in the paper. At 1550 nm, one 100 GHz channel spacing is approximately 0.8 nm, so two spacings correspond to about 1.6 nm, whereas 2.39 nm corresponds to three spacings. The text also says that crosstalk is negligible when there are 'at least two empty channels in between'; with the quantum signal at ITU channel 38, this means the classical signal at channel 41 or beyond, i.e., a separation of three ITU spacings, not two. The quantitative headline claim should be corrected and stated unambiguously.
  3. [§II, Eq. (8)] The initial condition for the quantum pulse contains a dimensional inconsistency. With τ defined in Section II as (t − z/v_g)/t0, the Gaussian factor in Eq. (8), exp(−τ^2/(2 t0^2)), has an exponent with dimensions of inverse time squared; if taken literally, the pulse has an unphysical temporal width rather than the nominal t0. The intended expression is almost certainly exp(−τ^2/2). Since this initial condition determines all reported crosstalk values, the discrepancy must be resolved before the numerical results can be reproduced or trusted.
  4. [§V, Eqs. (15)–(17), and §IV, Fig. 2] The stochastic equations contain noise terms, but the manuscript does not report the number of stochastic realizations, the step size Δζ, or any statistical error bars for the plotted crosstalk curves. If the curves in Figs. 2, 4, and 5 come from single realizations, the claimed quantitative behavior such as C ≈ 1 for distant channels and the monotonic power dependence is not fully supported. Ensemble averaging or at least error bars, together with convergence checks for the split-step scheme, are needed to substantiate the quantitative conclusions.
minor comments (5)
  1. [§II, Eq. (2)] The phase factor in Eq. (2), e^{i((k−k0)x+iω0t)}, mixes a spatial variable x with a time variable t and a plus sign; the propagation coordinate should be identified and the sign convention clarified.
  2. [Table I] The entry 't0 = √2 100 ps' lacks a multiplication symbol and is ambiguous; it should read '√2 × 100 ps' or equivalent.
  3. [§III, Eqs. (8)–(9)] The notation for frequency is inconsistent: Eq. (8) uses scaled frequencies Ωj and Ωq, while the filter in Eq. (9) is written using ω. This should be harmonized to avoid confusion.
  4. [§IV, Fig. 2] The caption says the classical channel is varied over the C-band, but the figure does not clearly label the axes or indicate whether the horizontal axis is ITU channel number, wavelength, or frequency; the units and axis labels should be added.
  5. [§IV, Fig. 3] The density plot caption does not state the color scale or the normalization of the plotted quantity, so the figure cannot be interpreted quantitatively; at minimum the color bar and the definition of the plotted field amplitude should be given.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the simulation uses an externally established stochastic GNLSE model with standard parameter values, and the crosstalk metric is an author-defined but independently computed observable.

full rationale

The paper's derivation chain is self-contained against external theory rather than circular. The propagation model in Eqs. (4a)-(4b) is taken from the established positive-P representation of quantum nonlinear fiber optics (ref. [25]), not from the paper's own results. The initial condition in Eq. (8) combines a standard 16-QAM classical signal and a Gaussian weak coherent pulse using standard fiber and system parameters (Table I: dispersion, Kerr coefficient, attenuation, channel spacing, pulse duration, photon number), with no parameter fitted to the crosstalk curves. The crosstalk metric C(ζ) in Eq. (10) is defined as the ratio of RMS temporal widths of the filtered quantum pulse with and without the classical signal, and the reported C values are numerical outputs of the simulation, not inputs used to adjust the model. The central claim that a separation of 2 ITU channels leads to negligible crosstalk therefore follows from the computed C, not from a definition that makes the result true by construction. The strongest concern in the manuscript is not circularity but external validity: the Outlook explicitly concedes that application-specific metrics such as quantum bit error rate should replace C(ζ), meaning the RMS-width measure may be insensitive to phase or frequency distortions that are relevant for QKD. That is a limitation of the chosen metric, not a circular reduction. The only self-citation is ref. [11] (Pathak, Chaudhary, et al.), used as background on phase-encoded QKD clock rates; it is not load-bearing for the derivation. No fitted-input-called-prediction, no imported uniqueness theorem, and no ansatz smuggled via self-citation are present. Accordingly, the paper is not circular and receives the lowest score.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard QNLSE formalism plus the paper's own RMS-width crosstalk metric and ideal-filter assumption. There are no fitted constants and no invented entities.

free parameters (5)
  • Average photon number per quantum pulse = 0.4
    Chosen as a typical weak coherent pulse for QKD; not fitted to crosstalk data.
  • Classical launch power P0 = 0.1 mW to 100 mW
    Swept input; the power dependence of crosstalk is one of the headline results.
  • Quantum pulse duration t0 = sqrt(2)*100 ps, with variations
    Chosen and then varied to study pulse-width dependence; not fitted.
  • 16-QAM bit rate Rc = 10 Gbps
    Representative classical line rate; no optimization against crosstalk data.
  • Fiber length L = 50 km
    Single-span representative reach; not fitted.
assumptions (5)
  • standard math The positive-P representation maps the quantum GNLSE to coupled stochastic PDEs with the stated noise correlations (Eqs. 4a, 4b).
    Taken from the Carter/Drummond references [25-27]; the paper does not rederive it.
  • domain assumption Raman scattering is negligible for the pulse widths and spectra considered.
    Stated in Section II; breaks for subpicosecond pulses, acknowledged in Section VI.
  • ad hoc to paper Crosstalk is adequately quantified by the RMS temporal width ratio C defined in Eq. (10).
    This metric is introduced by the authors; the paper itself says QBER is future work, so it is a load-bearing but unvalidated proxy.
  • domain assumption The quantum channel is recovered with an ideal rectangular spectral filter of width delta-omega (Eq. 9).
    Real WDM filters are not perfectly rectangular, and filter roll-off affects adjacent-channel leakage.
  • domain assumption Noise from inline amplifiers, polarization mode dispersion, Brillouin scattering, and other fiber impairments is absent.
    The model includes loss, Kerr nonlinearity, and dispersion only; deployed links typically have additional impairments.

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Cite this review

Pith. "Pith review of Robustness of WDM technique for the co-propagation of quantum with classical signals in an optical fiber." pith.science (2026). https://pith.science/paper/3XIDULIH

@misc{pith2026241116942,
  author       = {Pith},
  title        = {Pith review of: Robustness of WDM technique for the co-propagation of quantum with classical signals in an optical fiber},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3XIDULIH}},
  note         = {Machine review of arXiv:2411.16942}
}
read the original abstract

Many quantum communication systems operate based on weak light pulses which by design are assumed to operate in isolation from regular data traffic. With the widespread availability and commercialization of these systems comes a need for seamless integration already at the physical layer. In particular for optical fiber links where wavelength division multiplexing (WDM) is the dominant data transmission technique this results in the propagation of very weak quantum signals against a strong data signal background. With this work, we present a novel theoretical approach that studies the evolution of co-propagating quantum and classical signals that are launched using WDM. The important factors that contribute to crosstalk, such as the launch power of the classical signal and the separation between the two signals in terms of wavelength, are comprehensively analyzed. Interestingly, calculations show that only the first two nearest channels from the classical channel experience noticeable crosstalk whereas other distant channels have negligible crosstalk effect. This reflects the WDM technique is in principle robust in the integration of weak quantum links into classical data traffic.

Figures

Figures reproduced from arXiv: 2411.16942 by the authors.

Figure 1
Figure 1. Illustration of co-propagating quantum and classical signal in a [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Propagation of optical pulse representing the quantum signal in the [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Crosstalk effect when the classical channel is placed close to the [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: Effect of optical pulse width of the quantum signal on the crosstalk. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

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