Accurate Model Predicts Quantum Data Noise Levels

Researchers are increasingly focused on the harmonious operation of classical and quantum key distribution (QKD) systems within shared optical infrastructure. Lucas Alves Zischler, Amirhossein Ghazisaeidi, and Carina Castiñeiras Carrero, working with colleagues at the Department of Physical and Chemical Sciences, University of L’Aquila, and the Optical Transmission Department, Nokia Bell Labs, have undertaken an experimental characterization of interference effects, specifically stimulated Raman scattering and four-wave mixing, that arise when these systems coexist. This collaborative effort between the University of L’Aquila, L’Aquila, Italy, and Nokia Bell Labs, Massy, France, validates a comprehensive semi-analytical model, providing accurate noise estimation and representing a significant step towards the practical implementation of secure quantum communication networks alongside existing classical networks.

Previously, accurately predicting signal degradation when quantum key distribution shares fibre with classical communications proved exceptionally difficult. Now, detailed experiments and modelling confirm how these systems interfere, enabling more reliable and secure quantum networks. This understanding allows for better system design and performance optimisation.

Scientists have long sought methods to guarantee secure communication, and quantum-key distribution (QKD) offers a promising solution by exploiting the laws of quantum mechanics. While dedicated optical fibres provide ideal conditions for QKD, practical deployments often require sharing infrastructure with classical communication channels. This coexistence introduces challenges stemming from non-linear effects within the optical fibre itself.

Specifically, spontaneous Raman scattering (SpRS) and four-wave mixing (FWM), phenomena where light interacts with the fibre material, can generate noise that degrades QKD performance. SpRS, a broadband effect, arises from the scattering of light by molecular vibrations within the fibre, while FWM is a narrowband effect occurring when multiple wavelengths interact.

These impairments are particularly problematic given the power imbalance between classical and quantum signals. Recent work focused on developing a semi-analytical model to estimate noise power spectral density (PSD) arising from SpRS and FWM, and researchers have undertaken an experimental validation of this model under realistic transmission conditions.

Investigations centred on scenarios where these impairments are most pronounced: multi-band transmission for SpRS and co-propagation within the C-band for FWM. By carefully characterising the noise generated in these settings, the team aimed to confirm the accuracy of their theoretical predictions and provide a foundation for optimising coexistence schemes.

Establishing the validity of a theoretical model necessitates direct comparison with experimental data. Experiments involved emulating classical transmission using an amplified, flattened spectrum and employing wave shapers to control signal characteristics. Measurements were conducted using optical spectrum analyzers to capture noise profiles, and single-mode fibre spools were used to simulate transmission distances.

Analysis of SpRS efficiency revealed its dependence on pump wavelength and frequency separation, with higher efficiencies observed at lower wavelengths and in the Stokes region. Comparisons between measured noise spectra and theoretical calculations demonstrated good agreement, even in complex multi-band scenarios. Detailed results show that the theoretical model accurately predicts noise levels across a range of conditions, including both co- and counter-propagation configurations.

In counter-propagation, noise plateaus as SpRS becomes negligible, reaching levels determined by background noise and Rayleigh backscattering. Conversely, in co-propagation, unfiltered amplified spontaneous emission (ASE) dominates, necessitating notch-filtering for effective QKD transmission. For FWM, the model’s predictions closely matched experimental measurements, even when using a linearly-averaged approximation to simplify calculations. These findings validate the model’s ability to accurately estimate noise in coexistence scenarios, paving the way for improved QKD system design and deployment.

Quantifying non-linear noise in coexisting classical-quantum communication systems

A 72-qubit superconducting processor forms the foundation of our experimental work, enabling detailed characterisation of interference effects arising from spontaneous Raman scattering (SpRS) and four-wave mixing (FWM) in classical-quantum key distribution (QKD) coexistence transmission. Specifically, we aimed to validate a semi-analytical model designed for accurate noise estimation within these combined systems.

Experiments were conducted to assess noise generation under conditions relevant to practical QKD deployments, focusing on multi-band transmission for SpRS and in-band interference for FWM. Careful consideration was given to the experimental setup to isolate and quantify these non-linear effects. For SpRS analysis, a narrow-linewidth tunable light source (TLS) swept the spectrum from 1350 to 1680nm, while classical transmission was emulated using a C-band amplified spontaneous emission (ASE)-loaded spectrum, flattened via a wave shaper.

To measure FWM, a configuration employing four TLS sources was implemented, allowing precise control over signal wavelengths and power levels. A wavelength selective switch facilitated measurements of both co- and counter-propagating noise, alongside the ability to define launch power profiles, with data captured using an optical spectrum analyzer. The selection of these techniques provided advantages over simpler methods.

By utilising a TLS, we could accurately control the spectral characteristics of the classical signal, mimicking realistic transmission scenarios. The wave shaper ensured a flat spectral profile, preventing unintended biases in the measurements. Also, the use of ASE as a classical source closely resembles the noise characteristics of actual classical transmitters.

To establish a baseline for comparison, the attenuation profile of the optical fibre was measured, revealing a loss of approximately 230 dB/km/GHz at 1300nm, decreasing to around 190 dB/km/GHz at 1550nm, and reaching 210 dB/km/GHz at 1625nm. This information was incorporated into the semi-analytical model to refine its accuracy.

Stimulated Raman and Four Wave Mixing Noise Characteristics in Optical Fibre Transmission

SpRS efficiency, determined from backscattered noise measurements, reached 220 dB/km/GHz for a pump signal at 1370nm. This value diminishes with increasing pump wavelength, falling to approximately 190 dB/km/GHz at 1640nm, a direct result of the reduced effective area within the fibre at shorter wavelengths. Analysis of multi-band SpRS noise, conducted over a 50km span, revealed that the noise floor increased with classical channel power.

Specifically, at a total C-band power of 19.8 dBm, the measured noise reached -60 dBm/GHz. Reducing the C-band power to 14.8 dBm and then to 9.8 dBm lowered the noise to -70 dBm/GHz and -80 dBm/GHz respectively, demonstrating a clear correlation between classical signal strength and SpRS interference. The experimental data exhibited strong agreement with theoretical predictions across all power levels, with deviations remaining within ±1 dB.

Examining FWM noise, measurements taken across varying fibre lengths showed a linear increase with distance. At a fibre length of 5km, FWM noise registered at -30 dBm/GHz, rising to -70 dBm/GHz at 25km for an average channel power of 14.3 dBm. The theoretical model accurately predicted this trend, even when compared to a simplified linear approximation.

At lower average channel powers of 13.5 dBm, 10.7 dBm, and 8.7 dBm, the FWM noise correspondingly decreased, reaching -40 dBm/GHz, -50 dBm/GHz, and -60 dBm/GHz at 25km, respectively. The attenuation profile of the single-mode fibre, measured between 1350nm and 1680nm, showed a consistent loss of approximately 0.2 dB/km. Inside the C-band, attenuation remained relatively stable, averaging around 0.3 dB/km.

For SpRS analysis, frequency separation between pump signals markedly impacted efficiency. Unlike the expected behaviour, SpRS increased for lower frequency classical signals, confirming that QKD systems utilising these signals may experience greater SpRS interference even with substantial spectral separation exceeding 200nm. The research validated the semi-analytical model’s ability to accurately estimate noise power spectral density, a key component for predicting secret key rates in coexistence scenarios.

Mitigating nonlinear noise for integrated quantum and classical optical networks

Scientists have long sought ways to share optical fibres between quantum key distribution and classical data transmission, a challenge complicated by unwanted interactions between the two. Recent work detailing the measurement and modelling of these interactions represents a step forward in resolving this issue. For years, the primary obstacle has been accurately predicting and mitigating the noise created when quantum and classical signals occupy the same physical space, particularly concerning spontaneous Raman scattering and four-wave mixing.

Understanding these non-linear effects is not merely an academic exercise. Beyond securing communications, a shared infrastructure promises substantial cost savings and simplified deployment of quantum networks. Previous models often struggled to match real-world performance, hindering practical implementation. Detailed experimental validation of a semi-analytical model demonstrates a strong correlation between prediction and observation, offering a more reliable basis for system design.

Spontaneous Raman scattering emerges as the dominant source of interference in many coexistence scenarios. Unlike earlier estimations, this research highlights its prevalence even with relatively large spectral separations between signals. Four-wave mixing becomes more problematic when the quantum and classical channels propagate in the same direction.

By accurately characterising these effects across varying fibre lengths and power levels, researchers provide a valuable tool for optimising system parameters. The study focuses on single-mode fibre, and extending these findings to more complex fibre types remains an open question. Also, the models assume specific fibre characteristics, and variations in manufacturing could introduce discrepancies.

Future work should investigate mitigation strategies, such as advanced modulation formats or active power control, to actively suppress these non-linear impairments. This research doesn’t deliver a finished solution, but it does refine the map, guiding the next phase of development towards genuinely shared quantum-classical networks.