Performance of the subcarrier-wave quantum key distribution in the presence of spontaneous Raman scattering noise generated by classical DWDM channels

AI summary

Overview

Research area: Quantum communications — specifically quantum key distribution (QKD) co-existing with classical dense wavelength division multiplexing (DWDM) traffic in the same single-mode optical fiber, and the impact of spontaneous Raman scattering (SpRS) noise on a subcarrier-wave (SCW) QKD system.

Technical level: Intermediate. The paper relies on moderately advanced formalism (Wigner d-functions, the Devetak–Winter bound, binary symmetric erasure channel parameters), but the physical picture and the conclusions are stated in terms accessible to a reader with a general photonics or quantum-optics background.

Scope (one sentence): The paper builds a mathematical model of QBER and secure key rate for a subcarrier-wave QKD system impaired by Raman noise from 40 classical C-band DWDM channels, and compares continuous-wave versus pulsed source operation as a function of classical receiver sensitivity.

What This Paper Is About

Operators want to run QKD alongside ordinary data traffic in the same installed fiber, but classical laser channels are enormously brighter than quantum signals (the paper cites a typical 1 Gbps on-off-keying launch power of 0 dBm, equivalent to 8×10⁶ photons per pulse, versus a few tenths of a photon per pulse for the quantum signal). This brightness gap means noise processes such as spontaneous Raman scattering can bury the quantum signal. The authors ask a specific question that they state has not been studied in detail: how well does the subcarrier-wave variant of QKD survive SpRS noise from classical DWDM channels, and does it help to use a pulsed laser instead of a continuous-wave one?

Key Contributions

1. A mathematical model for the quantum bit error rate (QBER) of an SCW QKD system that explicitly adds SpRS noise, derived for two scattering geometries — forward-only scattering and combined forward-plus-backward ("full") scattering — starting from published expressions for forward and backward Raman noise power.

2. A secure key generation rate analysis based on the Devetak–Winter bound in the asymptotic limit of infinitely long keys, with the Holevo term taken from earlier collective beam-splitting attack results for the SCW protocol.

3. A direct comparison of two operating regimes of the same SCW setup — continuous-wave laser radiation (transmission window T = 10 ns) and pulsed radiation (T = 1 ns) — both modulated at the same 100 MHz rate of random phase shifts.

4. A numerical study of the maximum achievable distance (the distance at which the secret key rate is still positive) as a function of classical receiver sensitivity, spanning −23 dBm (typical of 1 Gbps OOK) to −48 dBm (typical of 40G/100G BPSK with coherent detection).

Main Findings

• Pulsed beats continuous-wave on every metric: The pulsed regime outperforms the continuous-wave regime in secure key generation rate, in QBER behavior, and in maximum achievable distance.

• Cause of the advantage: In the pulsed regime the pulse can be shaped so that the transmission window equals the detector gating time (τ = Δt/T = 1), whereas in the CW regime τ < 1 (here T = 10 ns versus Δt = 1 ns). The paper states that the click probability for the pulsed regime is ten times larger than in the CW regime, and that "the signal entirely fits into the gate."

• QBER rises quickly with fiber length under SpRS: The error rate approaches the critical value of approximately 0.07, at which a secret key can no longer be generated. The growth is fastest for the full (forward plus backward) scattering case, and in the CW regime the increase is so fast that, in the authors' words, the convex parts of the curves disappear.

• Key rate and distance collapse relative to the noise-free case: Compared with p_ram = 0, including SpRS produces a pronounced drop in maximum achievable distance, decreasing dramatically with forward scattering and further with full scattering.

• Headline distance numbers: At a classical receiver sensitivity of −28 dBm, the maximum distance is about 4 km for the CW setup and about 20 km for the pulsed setup. At −48 dBm, the pulsed SCW QKD maximum distance increases up to 90 km in the presence of SpRS noise from classical DWDM traffic.

• Better classical receivers help the quantum channel: Lowering the classical receiver sensitivity to −48 dBm reduces the required classical launch power, which increases the maximum distance and makes the effect of Raman scattering on the SCW system less pronounced. The maximum distance is described as a decreasing function of the receiver sensitivity value.

Methodology in Plain English

The authors do not build anything — this is a theory and simulation paper. They start from published formulas for the optical power of Raman-scattered light that lands in the quantum channel's filter band: one formula for light co-propagating with the classical channels, one for counter-propagating light (which has a sinh dependence on fiber length rather than a simple linear one). The classical channel output power is set by the receiver sensitivity plus the insertion losses of the system, so that classical communication still meets its bit-error-rate requirements. Converting Raman power into a detection probability is then straightforward: multiply by the gating time, divide by the single-photon energy at the quantum channel wavelength, and multiply by detector efficiency and the transmission of the insertion-loss elements.

Next they write the total click probability of the single-photon detector as three additive pieces: the conditional click probability from the weak quantum signal (computed from the SCW protocol's phase-modulation physics, where sidebands are generated and the carrier is suppressed by a spectral filter with attenuation ϑ), the dark-count probability, and the Raman probability. From clicks at the correct and incorrect Bob phase settings they define error and erasure probabilities, hence QBER. Inserting QBER into the Devetak–Winter formula, with error correction assumed to reach the Shannon bound and the Holevo information taken from prior beam-splitting attack analysis, gives the secret key rate. Sweeping fiber length yields curves from which they extract the maximum distance where the rate remains positive. A single set of system parameters is used throughout (40 classical channels spanning 1548.5–1564.3 nm, a quantum channel at 1535 nm, 15 GHz filter bandwidth, 0.18 dB/km fiber attenuation, 8 dB insertion loss, 4.8 GHz modulation frequency, μ₀ = 3.93, m = 0.319, ϑ = 10⁻³, Δt = 1 ns, η_D = 0.1, p_dark = 4×10⁻⁶, and a 5° phase mismatch).

Why This Matters

Impact on research: Subcarrier-wave QKD has an established protocol literature, but its behavior under DWDM co-existence noise had not been analyzed in detail. This paper supplies that missing piece and, more broadly, shows that the choice of source regime (CW versus pulsed) is a first-order design lever for Raman tolerance — potentially as important as narrow-band filtering, launch-power reduction, and temporal filtering, which the introduction lists as the standard mitigation techniques.

Real-world applications:

• Upgrading metropolitan and inter-data-center fiber links so that quantum keys are generated on the same strand as live customer traffic, avoiding the cost of dedicated dark fiber.
• Deploying QKD overlays onto existing 1 Gbps OOK access and enterprise networks, where the paper's −28 dBm receiver class applies and the reported CW distance of about 4 km versus pulsed distance of about 20 km is the design trade-off.
• Coherent 40G/100G backbone scenarios (BPSK with coherent detection, −48 dBm class), where the paper reports pulsed SCW QKD reaching up to 90 km alongside classical DWDM traffic.
• Guiding equipment choices: a pulsed source, rather than the continuous-wave source used in the experimental SCW implementations described in the paper, materially extends reach without changing the modulation rate.

Industry relevance: The result is a concrete engineering rule — match the transmission window to the detector gate — that costs nothing in hardware complexity class but buys roughly a factor of five in distance at −28 dBm and much more at −48 dBm. For operators deciding whether QKD can share installed C-band infrastructure, this is directly actionable.

Future Directions

• Experimental validation of the predicted 4 km / 20 km / 90 km figures on a real SCW testbed with live classical DWDM traffic, since all results here are numerical.
• Extending the security analysis beyond the asymptotic infinite-key limit to finite-key regimes, and beyond the collective beam-splitting attack model borrowed from prior work.
• Joint optimization of the pulsed regime's remaining free parameters (pulse width, mean photon number μ₀, modulation index m) now that τ = 1 is shown to be advantageous, and quantification of how much further the distance can be pushed.
• Broadening the impairment model to the other noise sources the introduction names — four-wave mixing, channel crosstalk, and amplified spontaneous emission from classical amplifiers — and comparing alternative channel allocations such as O-band quantum channels versus the C-band-everything scheme studied here.

Target Audience

Quantum communications researchers and graduate students working on QKD integration with classical optical networks; photonics and network engineers designing coexistence or overlay architectures for metro and backbone fiber; and system architects at telecom operators or vendors evaluating whether subcarrier-wave QKD can share installed C-band DWDM plant. Readers focused on experimental demonstrations or on protocols other than BB84-style SCW encoding will find modeling tools and a comparative result rather than measured data.

Authors’ abstract

In this paper we study performance of the subcarrier-wave quantum key distribution system (SCW QKD) in the presence of spontaneous Raman scattering (SpRS) noise generated by classical channels of dense wavelength division multiplexing (DWDM) network within a single-mode optical fiber. We present the mathematical model for evaluation of the quantum bit error rate (QBER) and the secure key generation rate with the SpRS noise taken into account. We consider two regimes of the SCW QKD system: the continuous wave regime that uses continuous wave laser and the pulsed regime. For these regimes, performance of the system is analyzed depending on receiver sensitivity of classical DWDM. It is found that the pulsed regime outperforms the continuous wave regime in both the secure key generation rate and the maximum achievable distance.