⚛️ quantum physics

Practical wavelength selection for quantum-augmented networks over shared optical fiber

This paper presents a wavelength-selection framework for quantum-augmented networks sharing optical fiber with classical traffic, demonstrating that optimal wavelengths for maximizing logical entanglement fidelity versus yield differ (1537 nm vs. 1551 nm) and identifying certified operating regions where high fidelity is maintained even as yield declines over long distances.

Original authors: Nitin Jha, Prateek Paudel, Abhishek Parakh

Published 2026-10-16

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Nitin Jha, Prateek Paudel, Abhishek Parakh

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world where the internet's security and speed are upgraded by a new kind of communication that relies on the strange laws of quantum physics. This is the promise of quantum-augmented networks, where delicate quantum signals travel alongside the massive, noisy flow of everyday data. The challenge is that these two types of traffic usually hate to share the same space. The powerful lasers sending standard internet data create a storm of interference that can drown out the faint, single particles of light used for quantum messages. To make them coexist, engineers must find a way to let them share the same glass fiber without the quantum signal getting lost in the noise.

The core of the problem is finding the right "color" of light, or wavelength, for the quantum message. If the quantum signal is too close in color to the classical data, the noise from the data will scramble the quantum information. If it is too far away, the equipment might not be able to handle it, or the signal might fade too quickly over long distances. Researchers have long known that they need to balance these factors, but they lacked a precise map to tell them exactly which color works best when the quantum signal has to travel back and forth multiple times through the same fiber, a process required for certain advanced security protocols.

A team of researchers at Kennesaw State University has now created a detailed framework to solve this puzzle. They focused on a specific setup where a quantum message travels from a sender to a receiver, bounces back to the sender, and then returns to the receiver one last time. This three-step journey is necessary for a particular type of error correction that helps protect the quantum information. The team built a computer model to simulate how different wavelengths of light would perform in this specific scenario, accounting for the real-world noise generated by the classical data traffic. They looked at how the fiber itself distorts the signal, how the lasers for the data create a background haze of stray light, and how the equipment filters out the unwanted noise.

Their simulations revealed a surprising truth: the best color for the quantum signal depends entirely on what you are trying to optimize. If the goal is simply to ensure the quantum message arrives with the highest possible purity and accuracy, the ideal wavelength is near 1537 nanometers. However, if the goal is to maximize the number of successful messages that get through, even if they are slightly less pure, the best choice shifts to a different color near 1551 nanometers. This distinction is crucial because it shows that there is no single "perfect" setting for all situations; network operators must decide whether they prioritize the absolute quality of the connection or the sheer volume of data they can send.

The study also mapped out exactly how far these signals can travel before the connection breaks down. For a standard internet data rate of 1.25 gigabits per second, the researchers found that the system can maintain a certified, high-quality connection over distances of 10 kilometers or more, provided the quantum signal is sent at the right wavelength. However, as the distance increases, the number of successful messages drops sharply. At the 10-kilometer mark, the system can still guarantee that the quantum information is preserved with a fidelity of 99 percent or higher, but the rate at which these successful messages arrive becomes very low. This means that while the connection is technically possible over long distances, it becomes much less efficient.

The researchers also tested how sensitive this system is to changes in the environment. They found that if the background noise from the classical data increases even slightly, or if the equipment has small imperfections, the entire system can fail to meet the strict requirements for a secure connection. This suggests that in a real-world deployment, the equipment would need to be carefully calibrated and the network conditions monitored constantly. The study confirms that while sharing fiber is possible, it requires a very precise selection of the quantum wavelength, one that changes depending on the distance and the power of the classical data being sent.

Ultimately, this work provides a practical guide for engineers building the next generation of secure networks. It moves beyond the idea that quantum and classical signals can just be mixed together and shows that they require a carefully choreographed arrangement. By identifying the specific wavelengths that work best for different goals, the researchers have given network designers the tools to build systems that are both secure and efficient. The findings confirm that while the path is narrow and the conditions are strict, it is possible to run these advanced quantum networks over the existing fiber infrastructure that already crisscrosses our cities, provided we know exactly which color of light to use.

Technical Summary: Practical Wavelength Selection for Quantum-Augmented Networks over Shared Optical Fiber

Problem Statement
The integration of quantum communication into existing optical infrastructure requires sharing fiber with high-power classical traffic. While dedicated fibers isolate quantum signals, they increase deployment costs and limit infrastructure reuse. Wavelength-division multiplexing (WDM) offers an alternative but introduces fundamental asymmetry: classical channels operate at power levels orders of magnitude higher than quantum signals. This coexistence generates significant noise at the quantum receiver, primarily through Spontaneous Raman Scattering (SpRS), Four-Wave Mixing (FWM), filter leakage, and Cross-Phase Modulation (XPM).

Existing wavelength-allocation studies often focus on Quantum Key Distribution (QKD) metrics like Quantum Bit Error Rate (QBER) or secret-key rate. However, for encoded quantum communication protocols involving repeated channel traversals (such as the three-stage protocol), simple noise minimization is insufficient. The selection of a quantum wavelength must simultaneously satisfy:

Classical Link Budget: Ensuring sufficient launch power for classical data reception.
Logical Fidelity: Maintaining the integrity of the encoded logical qubit after error correction.
Block Acceptance: Ensuring the receiver successfully detects the photon without being overwhelmed by background noise.

Crucially, the wavelength that minimizes optical noise (maximizing fidelity) may not maximize the probability of block acceptance, and vice versa. This paper addresses the need for a unified framework to select wavelengths that optimize the "entanglement-fidelity yield" (the product of acceptance probability and logical fidelity) under these competing constraints.

Methodology
The authors develop an optical-to-logical framework for a CSS-encoded three-stage quantum communication protocol sharing fiber with a fixed classical WDM deployment.

System Model: The system involves Alice and Bob exchanging a quantum signal over a single-mode fiber in three traversals (Alice→Bob, Bob→Alice, Alice→Bob). Classical channels co-propagate during traversals 1 and 3, and counter-propagate during traversal 2.
Noise Modeling: The framework maps wavelength-dependent optical impairments to a physical qubit channel:
- Spontaneous Raman Scattering (SpRS): Modeled as additive thermal background, calculated based on the Raman gain spectrum of fused silica and the Bose-Einstein occupation number.
- Four-Wave Mixing (FWM): Calculated based on classical carrier frequencies, fiber nonlinearity ( $\gamma$ ), and phase-matching conditions.
- Filter Leakage: Modeled as classical power leaking through imperfect isolation.
- Cross-Phase Modulation (XPM): Treated as differential polarization phase noise, modeled as a stochastic phase fluctuation affecting the qubit state.
Receiver Model: An ideal one-photon receiver is assumed. It accepts the one-photon subspace after the final traversal. The model distinguishes between block acceptance (detecting a photon) and state preservation (maintaining the input qubit state). Background photons can contribute to acceptance but degrade fidelity.
Logical Layer: The study utilizes the Steane [[7,1,3]] CSS code. The framework derives a lower bound on the conditional logical entanglement fidelity ( $C_{n,t}(q)$ ) after ideal recovery, where $q$ represents the probability of a non-identity error event per physical qubit.
Optimization Objective: The authors define an "entanglement-fidelity yield" ( $Y$ ) as the product of block acceptance probability ( $s^n$ ) and the lower bound on logical fidelity. The objective is to maximize this yield subject to a minimum fidelity certificate ( $F_{min}$ ) and the classical link budget.

Key Contributions

Unified Framework: The paper derives a closed-form accepted optical qubit channel and a key-independent lower bound on logical entanglement fidelity for a three-stage protocol with CSS error correction.
Distinction of Metrics: It explicitly demonstrates that maximizing fidelity (minimizing noise) and maximizing yield (balancing acceptance and fidelity) can lead to different optimal wavelengths.
Certified Operating Regions: The work defines "certified operating regions" where specific wavelengths satisfy both fidelity and yield requirements under a thermal-background model with independent errors.
Sensitivity Analysis: The framework evaluates the impact of tuning clearance, Raman levels, base errors, and XPM on the viability of wavelength selection.

Results
Numerical simulations were performed for the Steane [[7,1,3]] code with a target fidelity of $F_{min} = 0.99$ and a yield threshold of $Y_{min} = 10^{-6}$ .

Wavelength Divergence: At a specific operating point (5 km per traversal, -10 dBm classical launch power), the wavelength maximizing the fidelity certificate is 1537.011 nm, whereas the wavelength maximizing the yield bound is 1551.327 nm. The latter coincides with the choice that maximizes transmission (minimizes loss), indicating that higher acceptance probability can outweigh a slightly lower fidelity certificate in the yield metric.
Distance and Power Constraints:
- Along a 1.25 Gb/s classical link budget with a 0.2% base error, the optimized yield bound drops below $10^{-6}$ near 10 km per traversal.
- However, the fidelity remains certified (≥ 0.99) even at spans longer than 10 km, suggesting that the yield requirement (block acceptance) is the limiting factor for operation at longer distances, not the fidelity requirement.
Sensitivity:
- Doubling the Raman noise level or the base error removes all fidelity-certified candidates at the reference point, highlighting the need for precise calibration.
- Increasing the guard band (tuning clearance) from 0 to 5 GHz results in a negligible yield penalty (< 0.5%) at 3 km and 5 km, though it shifts the selected wavelength by approximately 0.8 nm.
- The admissible base error decreases as distance and launch power increase; at 10 km, even a 0.2% base error fails to meet the yield threshold.

Significance and Claims
The paper claims to provide a practical methodology for selecting quantum wavelengths in shared-fiber networks by distinguishing between fidelity constraints and yield constraints. It identifies that for protocols involving repeated traversals and error correction, the optimal wavelength is not simply the one with the lowest noise, but the one that maximizes the product of acceptance and logical fidelity.

The authors state that their results allow for the identification of "certified operating regions" where quantum-augmented networks can operate alongside classical traffic. The key-independent fidelity certificate allows network gateways to assess whether a communication link can meet its requirements without knowing the specific private transformation keys used in the protocol. The work concludes that while the thermal-background and independence assumptions require further experimental validation, the derived criteria offer a necessary foundation for the engineering of quantum-augmented networks sharing optical infrastructure.

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