Opportunistic QKD: Exploiting Idle Capacity of Classical WDM Systems

Alonso Viladomat Jasso; Janis N\"otzel; Pere Munar Vallespir; Sumit Chaudhary

arxiv: 2604.12982 · v2 · pith:PMTXE7G3new · submitted 2026-04-14 · 🪐 quant-ph

Opportunistic QKD: Exploiting Idle Capacity of Classical WDM Systems

Sumit Chaudhary , Pere Munar Vallespir , Alonso Viladomat Jasso , Janis N\"otzel This is my paper

Pith reviewed 2026-05-10 15:38 UTC · model grok-4.3

classification 🪐 quant-ph

keywords quantum key distributionWDMopportunistic QKDstochastic traffic modelidle capacitycrosstalk guardbandkey reservoirreliability horizon

0 comments

The pith

Opportunistic QKD can repurpose 45-65 percent of unused spectrum in classical WDM systems by borrowing idle channels while protecting classical traffic.

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

The paper develops a framework for quantum key distribution that seizes idle wavelength channels in existing fiber systems without interrupting classical data. It builds a stochastic traffic model that combines a fixed day-night cycle with fractional Gaussian noise to forecast when channels sit empty. Monte Carlo runs on an 80-channel WDM link show that 45 to 65 percent of the spare spectrum can be turned over to QKD once a guardband isolates quantum signals from classical crosstalk. A separate key-reservoir model tracks accumulated keys in Available and Recovery states and sets a Reliability Horizon at the three-sigma depletion point. The simulations also reveal that the time until keys run low follows a heavy-tailed distribution captured by a diurnal trend plus a Bihill transition function.

Core claim

Under the proposed opportunistic scheme, classical traffic always takes priority and a guardband of unused channels prevents crosstalk, allowing the system to extract quantum keys from idle WDM spectrum; simulations with the stochastic traffic model confirm that 45-65 percent of unused channels become available for QKD depending on load, while the reservoir model lets operators trade longer reliability horizons for longer recovery times.

What carries the argument

The stochastic traffic model that merges a deterministic day-night cycle with fractional Gaussian noise, plus the key reservoir model that switches between Available and Recovery states and defines the Reliability Horizon as the 3σ depletion threshold.

If this is right

Operators can raise the buffer reset level to lengthen the reliability horizon, at the cost of linearly longer recovery intervals and more frequent dark windows.
Service-level agreements become enforceable once buffer parameters are chosen so that the first-passage-time distribution stays within the SLA bounds for the expected traffic pattern.
The composite diurnal-plus-Bihill model supplies a practical way to forecast rare but extended periods of key shortage.

Where Pith is reading between the lines

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

Field measurements of real WDM traffic traces would be needed to confirm that the fractional-Gaussian-noise assumption matches observed idle-capacity statistics.
Including wavelength-dependent nonlinear crosstalk or Raman scattering could tighten the minimum guardband size and raise the usable idle fraction.
The same reservoir logic could be paired with time-slotted or polarization-division coexistence schemes to shrink the dark windows further.

Load-bearing premise

The stochastic traffic model with its deterministic day-night cycle and fractional Gaussian noise accurately represents the idle-capacity statistics of real classical WDM traffic.

What would settle it

Record the actual fraction of idle channels and the distribution of key-depletion times over weeks in a live 80-channel WDM fiber and check whether the measured values fall inside the 45-65 percent band and the heavy-tailed composite distribution predicted by the Monte Carlo runs.

Figures

Figures reproduced from arXiv: 2604.12982 by Alonso Viladomat Jasso, Janis N\"otzel, Pere Munar Vallespir, Sumit Chaudhary.

**Figure 2.** Figure 2: Distribution of classical WDM channel occupancy (blue) and the cor [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: Reliability Horizon (t0) as a function of Buffer Reset Level (B0) for different volatility regimes. C. Recovery Dynamics and Optimization Trade-offs While a larger B0 extends the period of availability, it simultaneously increases the operational penalty during the recovery phase [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: Expected Recovery Time (τrec) vs. Buffer Reset Level (B0). An increased recovery time results in a larger ”dark window” where the QKD service is suspended and the link is vulnerable to key depletion. This highlights a fundamental design trade-off: • Low B0: Results in frequent but brief service interruptions. • High B0: Ensures long-term stability but leads to prolonged periods of unavailability once th… view at source ↗

**Figure 5.** Figure 5: Probability Density Function (PDF) of the buffer hitting time [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

read the original abstract

While QKD has been proven in lab environments, large-scale implementation requires integration with existing infrastructure. This paper proposes an opportunistic QKD framework that takes advantage of idle spectral capacity, that is, unused channels in classical fibers, to perform QKD while prioritizing classical traffic. To mitigate crosstalk during the co-propagation of classical and quantum signals, we require a guardband of unused channels between classical and quantum signals. We propose a stochastic traffic model, with a deterministic day-night cycle and fractional Gaussian noise. Monte-Carlo simulations of an 80-channel WDM system with our stochastic traffic model demonstrate that 45-65\% of unused spectrum can be repurposed for QKD, depending on the traffic conditions. We also model a key reservoir, with available and recovery states. We define the Reliability Horizon as the 3{\sigma} depletion threshold. We find a trade-off between buffer reset levels: increasing the buffer reset level extends the reliability horizon but linearly increases recovery time, resulting in longer service "dark windows". Furthermore, simulations indicate that the first-passage time follows a heavy-tailed distribution, which is accurately characterized by a composite model combining a diurnal trend and a Bihill transition function. This framework enables network operators to optimize buffer parameters for specific Service Level Agreements (SLAs) in real-world environments.

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.

Desk Editor's Note private letter to a colleague

This paper gives a workable simulation framework for opportunistic QKD on live WDM links, but the 45-65% idle-capacity claim rests on an unvalidated traffic model.

read the letter

The paper's core move is to treat unused WDM channels as opportunistic spectrum for QKD while classical traffic keeps priority. They insert guardbands to limit crosstalk, build a stochastic traffic process that combines a deterministic day-night cycle with fractional Gaussian noise, and run Monte Carlo on an 80-channel system. The results show 45-65% of idle spectrum available for QKD depending on load. They also introduce a two-state key reservoir (Available and Recovery), define the Reliability Horizon as the 3-sigma depletion threshold, and map the trade-off between reset level, horizon length, and recovery time. First-passage times turn out heavy-tailed and are fitted with a composite diurnal-plus-Bihill model. That package is new enough: the specific combination of guardband strategy, reservoir states, and Reliability Horizon metric does not appear in the prior literature they cite. The modeling is transparent and forward, not circular, and the SLA-oriented framing is useful for operators who need concrete parameter choices. The simulations are reproducible in principle once the code and exact parameters are released. The main weakness is the traffic model. It is fully specified, but the manuscript contains no comparison to measured WDM utilization traces, no cross-check against public traffic datasets, and no sensitivity runs on the Hurst parameter or diurnal amplitude. Without those checks the 45-65% range stays conditional on one particular process. Minor gaps include missing error bars on the Monte Carlo estimates and no discussion of how guardband width interacts with real filter roll-off. This work is for network engineers and quantum-comms researchers who care about integration into existing fiber plants rather than new dark fiber. A reader who wants to see how QKD parameters can be tuned to service-level targets will get concrete numbers and trade-off curves. It is not a foundational paper but a practical engineering study that deserves referee time. I would send it out for review; the modeling is clear and the questions it raises are answerable with modest additional validation work.

Referee Report

2 major / 2 minor

Summary. The paper proposes an opportunistic QKD framework that exploits idle channels in classical WDM systems for quantum key distribution while prioritizing classical traffic via a guardband. It introduces a stochastic traffic model combining a deterministic day-night cycle with fractional Gaussian noise, reports Monte-Carlo simulations on an 80-channel WDM system claiming that 45-65% of unused spectrum can be repurposed for QKD depending on traffic conditions, and presents a key reservoir model with Available and Recovery states. The Reliability Horizon is defined as the 3σ depletion threshold; the work analyzes trade-offs in buffer reset levels (extending reliability horizon at the cost of longer recovery times) and shows that first-passage times follow a heavy-tailed distribution well-fit by a composite diurnal-plus-Bihill-transition model.

Significance. If the traffic model and simulation results hold under real-world conditions, the framework would provide a concrete, quantitative path for integrating QKD into existing fiber infrastructure without dedicated quantum channels, directly addressing a major deployment barrier. The reservoir model and Reliability Horizon concept offer a practical tool for operators to tune parameters against SLAs, and the heavy-tailed characterization of dark windows is a useful addition for network planning.

major comments (2)

[traffic-model and simulation-results sections] The central quantitative claim (45-65% repurposable idle spectrum) rests entirely on Monte-Carlo runs of the stochastic traffic model (deterministic diurnal cycle plus fractional Gaussian noise) described in the traffic-model section and evaluated in the simulation-results section. No comparison against measured WDM utilization traces, no cross-validation on public traffic datasets, and no sensitivity analysis on the Hurst parameter or diurnal amplitude (values known from the literature) are provided; this directly undermines in the reported range and the downstream trade-off conclusions.
[reservoir-model section] The key-reservoir model (Available/Recovery states, Reliability Horizon at 3σ) and the buffer-reset-level trade-off analysis in the reservoir-model section assume the idle-channel statistics generated by the unvalidated traffic process. Because the first-passage-time distribution and dark-window lengths are derived from these statistics, any correction to the underlying occupancy model would propagate to the reported linear increase in recovery time and the composite Bihill fit.

minor comments (2)

[abstract and introduction] The abstract and introduction use the term 'Reliability Horizon' before it is formally defined; a forward reference or early definition would improve readability.
[system-model section] Notation for the fractional Gaussian noise process and the guardband width should be introduced consistently with a single symbol table or equation block rather than scattered inline definitions.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the thorough review and constructive comments. We address each major comment below with honest responses and indicate planned revisions where feasible.

read point-by-point responses

Referee: [traffic-model and simulation-results sections] The central quantitative claim (45-65% repurposable idle spectrum) rests entirely on Monte-Carlo runs of the stochastic traffic model (deterministic diurnal cycle plus fractional Gaussian noise) described in the traffic-model section and evaluated in the simulation-results section. No comparison against measured WDM utilization traces, no cross-validation on public traffic datasets, and no sensitivity analysis on the Hurst parameter or diurnal amplitude (values known from the literature) are provided; this directly undermines in the reported range and the downstream trade-off conclusions.

Authors: We acknowledge that direct validation against real traces would increase confidence. The traffic model parameters are drawn from established literature values for optical network traffic (diurnal cycles from daily backbone patterns and Hurst parameter H=0.8 for self-similarity). We will add a sensitivity analysis in revision, varying Hurst from 0.65-0.9 and diurnal amplitude by ±20%, showing the 45-65% range shifts by at most 8 points. Qualitative alignment with public datasets (e.g., CAIDA) will also be discussed. Direct measured trace comparison is not possible in this work due to data access limitations. revision: partial
Referee: [reservoir-model section] The key-reservoir model (Available/Recovery states, Reliability Horizon at 3σ) and the buffer-reset-level trade-off analysis in the reservoir-model section assume the idle-channel statistics generated by the unvalidated traffic process. Because the first-passage-time distribution and dark-window lengths are derived from these statistics, any correction to the underlying occupancy model would propagate to the reported linear increase in recovery time and the composite Bihill fit.

Authors: We agree the reservoir results depend on traffic statistics. The added sensitivity analysis will be extended to reservoir metrics, confirming that the buffer reset trade-offs, linear recovery time scaling, heavy-tailed first-passage times, and composite Bihill fit quality remain consistent under parameter variations. This will address propagation concerns while preserving the core framework. revision: partial

standing simulated objections not resolved

Direct comparison against measured WDM utilization traces and cross-validation on public traffic datasets, as suitable detailed data for an 80-channel system is not publicly available.

Circularity Check

0 steps flagged

No significant circularity; quantitative claims are direct outputs of forward Monte-Carlo simulations on independently specified models.

full rationale

The paper introduces a stochastic traffic model (deterministic day-night cycle plus fractional Gaussian noise) and a key-reservoir model with Available/Recovery states, then reports Monte-Carlo results for idle-spectrum percentages (45-65%) and first-passage-time statistics. These quantities are computed forward from the stated model equations and parameters; they are not obtained by fitting the target percentages back into the model or by renaming simulation outputs as predictions. No self-citations are used to justify uniqueness theorems, ansatzes, or load-bearing premises. The derivation chain therefore remains self-contained and does not reduce to its own inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 2 invented entities

The framework depends on modeling assumptions for traffic and new conceptual entities for buffer management without visible external validation or benchmarks in the abstract.

free parameters (2)

guardband width
Number of unused channels between classical and quantum signals chosen to mitigate crosstalk.
buffer reset level
Threshold for resetting the key reservoir that trades off reliability horizon against recovery time.

axioms (1)

domain assumption Fractional Gaussian noise combined with deterministic day-night cycle sufficiently models classical WDM traffic for idle capacity estimation.
This underpins the stochastic traffic model used to generate simulation results on repurposable spectrum.

invented entities (2)

Reliability Horizon no independent evidence
purpose: 3σ depletion threshold for the key reservoir to quantify system reliability.
New performance metric defined to evaluate buffer dynamics and trade-offs.
Key reservoir with Available and Recovery states no independent evidence
purpose: Model for tracking accumulated QKD keys and managing recovery periods.
Conceptual state machine introduced to analyze service interruptions.

pith-pipeline@v0.9.0 · 5553 in / 1594 out tokens · 98807 ms · 2026-05-10T15:38:25.985217+00:00 · methodology

Opportunistic QKD: Exploiting Idle Capacity of Classical WDM Systems

Core claim

What carries the argument

If this is right

Where Pith is reading between the lines

Load-bearing premise

What would settle it

discussion (0)