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Scientific Reports

Improving the performance of practical wavelength division multiplexing decoy-state quantum key distribution with advantage distillation

Bumil Kim, Jun Heo

Published May 22, 2026• 0 citations
Publisher

Abstract

Quantum key distribution (QKD) is a promising method for sharing an information-theoretically secure secret key using the properties of quantum mechanics. Although QKD is the most practical field in quantum information science, its widespread adoption is constrained by high implementation costs. Despite the cost-effectiveness of propagating QKD with classical communication using wavelength division multiplexing (WDM), the noise generated by relatively strong classical signals degrades QKD performance. Even though several mitigation strategies exist, they often involve complexity or additional hardware. In this paper, we apply advantage distillation (AD) to enhance the performance of a practical decoy-state BB84 QKD system operating in a WDM environment. We perform finite-key analysis in both co-propagation and counter-propagation scenarios with three classical channels, and furthermore we examine the effects of varying the number of classical channels and the optical power per channel. A comparison of simulation results obtained with and without AD demonstrates that AD is robust to noise originating from classical channels. These results show that AD increases the secure key rate and transmission distance in the WDM-based QKD environment under both co-propagation and counter-propagation without requiring hardware changes. These findings suggest advantage distillation is a promising strategy for the widespread adoption of WDM-based QKD, including in challenging counter-propagation cases.

DOI
10.1038/s41598-026-52452-4

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Quantum key distribution (QKD) is a promising method for sharing an information-theoretically secure secret key using the properties of quantum mechanics. Although QKD is the most practical field in quantum information science, its widespread adoption is constrained by high implementation costs. Despite the cost-effectiveness of propagating QKD with classical communication using wavelength division multiplexing (WDM), the noise generated by relatively strong classical signals degrades QKD performance. Even though several mitigation strategies exist, they often involve complexity or additional hardware. In this paper, we apply advantage distillation (AD) to enhance the performance of a practical decoy-state BB84 QKD system operating in a WDM environment. We perform finite-key analysis in both co-propagation and counter-propagation scenarios with three classical channels, and furthermore we examine the effects of varying the number of classical channels and the optical power per channel. A comparison of simulation results obtained with and without AD demonstrates that AD is robust to noise originating from classical channels. These results show that AD increases the secure key rate and transmission distance in the WDM-based QKD environment under both co-propagation and counter-propagation without requiring hardware changes. These findings suggest advantage distillation is a promising strategy for the widespread adoption of WDM-based QKD, including in challenging counter-propagation cases.
Wavelength division multiplexing (WDM) of quantum key distribution (QKD) with classical optical channels has been proven to be feasible experimentally. In this paper, we will analyze the practical security of WDM-QKD theoretically. Specifically, we first establish the noise model of classical signals. Then, the influence of classical noises on the performance of decoy-state WDM-QKD is studied with a finite-key security analysis. For numerical simulations, the effect of classical noise-reduction methods for different experimental settings is given. The secret key rate and maximum transmission distance of WDM-QKD is simulated with various sent number of quantum pulses or transmitted power of classical signals. Furthermore, the performance of two kinds of decoy-state WDM-QKD is compared, which shows that the optimal decoy-state protocol for WDM-QKD is related to the sent number of quantum pulses. Since WDM-QKD is desired to reduce the cost of QKD networks and since experiments have already been carried out, our work can not only close the gap between theory and practice, but also be used to optimize the experimental parameters and improve its performance.
Entanglement-based quantum key distribution (EB-QKD) is considered an important implementation method for fully connected quantum networks. Due to practical considerations for conserving fiber resources, the demand for integrating EB-QKD into existing optical networks through wavelength-division multiplexing (WDM) in the same fiber (referred to as EB-WDM-QKD) is increasingly urgent. However, the noise generated from the classical system is an inherent limitation that restricts the performance of EB-WDM-QKD. In this work, we proposed an improved scheme that employs optical amplifiers to enhance the performance of EB-WDM-QKD. Under the fixed classical received power scenario, the transmission distance can be increased by more than 70 km compared to the original EB-WDM-QKD scheme without amplifiers. Moreover, for the scenario where the launch power of data lasers and amplifiers in the classical channel is non-adjustable, we applied the advantage distillation (AD) method to further enhance the performance of EB-WDM-QKD, and the transmission distance can be enhanced by more than 50 km. Our work can significantly enhance the performance of the EB-WDM-QKD system by optimizing the configuration of the classical subsystem and the post-processing of the quantum subsystem. The methods have the potential to be extended to various WDM-QKD systems, providing new perspectives for the advancement of WDM-QKD.
Quantum Key Distribution (QKD) allows two legitimate parties, Alice and Bob, to share a secret key with information-theoretic security, ensuring that an eavesdropper, Eve, cannot obtain any information about the key. A QKD protocol is provably secure only when the Quantum Bit Error Rate (QBER) is below a certain threshold and, therefore, the presence of noise inherently limits the maximum transmission distance. Advantage Distillation (AD) is a classical post-processing technique that enhances QKD protocols by increasing the maximum acceptable QBER and, thus, allows extending the communication range. AD operates by post-selecting blocks of bits and extracting fewer but highly correlated bits between Alice and Bob, which exhibit a reduced QBER, thus lowering the amount of information that has to be disclosed during the information reconciliation step. In this study, we present a new analytical expression for the secure key rate. This will enable a finite-size secure key length analysis of the decoy state version of the BB84 protocol including AD post-processing.
Advantage Distillation (AD) is a classical post-processing technique that enhances Quantum Key Distribution (QKD) protocols by increasing the maximum acceptable Quantum Bit Error Rate (QBER) and thus extending the distance at which QKD links can be securely established. AD operates by post-selecting blocks of bits and extracting fewer high-fidelity bits, exhibiting a reduced QBER and thus lowering the amount of information that has to be disclosed during the information reconciliation step. In this work we present the first comprehensive finite key-size analysis of decoy-state BB84 enhanced via AD post-processing. We demonstrate that through the use of AD the maximum acceptable QBER increases from around 9.5%9.5\%9.5% to around 17.3%17.3\%17.3% for realistic key sizes. This result shows that substantial performance enhancements can be achieved in scenarios which are constrained by the maximum tolerable QBER via improvements of the post-processing method alone.
The integration of quantum key distribution (QKD) devices with the existing optical fiber networks is of great significance in reducing the deployment costs and saving fiber resources. Wavelength division multiplexing (WDM) is expected to be a desirable approach to fulfill this ultimate task. In this paper, we analyze the dominant noises in WDM-based QKD system and optimize the key parameters based on a modified model with 200 GHz channel spacing. Then, an appropriate decoy-state method is adopted to estimate the system performance considering statistical fluctuations. Finally, a three-layer artificial neural network is used to train and predict the optimal mean photon numbers within different situations. Our work provides a useful method for the parameters optimization of WDM-QKD system and accelerates the practical development of QKD that coexists with the current backbone fiber infrastructure.
Quantum key distribution (QKD) has been extensively studied for practical applications. Advantage distillation (AD) represents a key technique to extract highly correlated bit pairs from weakly correlated ones, thus improving QKD protocol performance, particularly in large-error scenarios. However, its practical implementation remains under-explored. In this study, the AD is integrated into the three-intensity decoy-state BB84 protocol and its performance is demonstrated on a high-speed phase-encoding platform. The experimental system employs an asymmetric Mach-Zehnder interferometer (AMZI) fabricated on a silicon dioxide optical waveguide chip for phase encoding, which is benefited from its low coupling loss and minimum waveguide transmission loss. Phase-randomized weak coherent pulses, generated by a distributed feedback laser at 625 MHz, are modulated into decoy states of varying intensities. The signals are encoded via an AMZI and attenuated to single-photon levels before transmission. At the receiver, another AMZI demodulates the signals detected by avalanche photodiodes in gated mode. Experiments conducted at 50 km and 105 km demonstrate secure key rates of 104 kbits/s and 59 bits/s, respectively. The results at shorter distances closely match theoretical predictions, while slight deviations at 105 km are attributed to signal attenuation and noise. Despite these challenges, the results obtained at 105 km highlight the effectiveness of AD in enhancing secure key rates in the large-error scenario. This study confirms the potential of AD in extending secure communication range of QKD. By leveraging the high integration and scalability of silicon dioxide photonic chips, the proposed system lays a foundation for large-scale QKD deployment, paving the way for developing advanced protocols and real-world quantum networks.