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IEEE Access

Adaptation of Error Correction Procedures to the Time-Bin Quantum Key Distribution Protocol Implementation

Vladimir Morozov, Mikhail S. Elezov, Oleg Olegovich Evsutin, Roman V. Ozhegov

Published Dec 26, 2025• 1 citation
Publisher

Abstract

Error correction is a crucial stage in quantum key distribution (QKD) protocols—a promising field of modern cryptography where the secrecy of the shared key information is guaranteed by the laws of quantum mechanics. Currently, there are many effective approaches to error correction in QKD. However, most of them, due to their generic nature, fail to leverage the specific features of particular protocol implementations. This work demonstrates that accounting for the hardware specifics of a QKD system implementing the time-bin protocol enables a significant increase in error correction performance. For the considered QKD system, we have experimentally obtained estimates of the Quantum Bit Error Rate (QBER) observed for each combination of bit and detector. The differences in the obtained estimates reveal that the quantum channel can be modeled as a non-uniform binary channel. Furthermore, based on computational experiments with a model of the quantum channel, it was established that adapting the error correction procedure to its properties can achieve up to a 2.7-fold reduction in the LDPC code decoding failure rate at low error levels.

DOI
10.1109/access.2025.3648803

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Error correction is a crucial stage in quantum key distribution (QKD) protocols—a promising field of modern cryptography where the secrecy of the shared key information is guaranteed by the laws of quantum mechanics. Currently, there are many effective approaches to error correction in QKD. However, most of them, due to their generic nature, fail to leverage the specific features of particular protocol implementations. This work demonstrates that accounting for the hardware specifics of a QKD system implementing the time-bin protocol enables a significant increase in error correction performance. For the considered QKD system, we have experimentally obtained estimates of the Quantum Bit Error Rate (QBER) observed for each combination of bit and detector. The differences in the obtained estimates reveal that the quantum channel can be modeled as a non-uniform binary channel. Furthermore, based on computational experiments with a model of the quantum channel, it was established that adapting the error correction procedure to its properties can achieve up to a 2.7-fold reduction in the LDPC code decoding failure rate at low error levels.
Quantum Key Distribution (QKD) is a promising field in modern cryptography where the security of key information is guaranteed by the laws of quantum mechanics. One of the key stages in QKD protocols is error estimation and reconciliation in the secret key. This procedure requires the transmission of a certain number of secret key bits over a public channel. Such transmission leads to disclosing these bits to a potential eavesdropper. The fraction of disclosed bits—the sampling rate-largely depends on the chosen approach for preliminary error estimation in the channel. This work is devoted to the optimization of the sampling rate for an LDPC code from the 5G\mathbf{5 G}5G standard. The results of our experiments show that for a QBER below 0.2 and key lengths of 264, 528, 792, and 1056 bits, it is necessary to disclose no more than 18%,11%,10%18 \%, 11 \%, 10 \%18%,11%,10%, and 7%7 \%7% of the key bits for error estimation, respectively. Furthermore, the proposed algorithm allows for similar optimization for any information reconciliation protocols and actual quantum bit error rates.
The purpose of reconciliation, one of classical aspects of quantum key distribution (QKD) protocol, is to mitigate errors after the distribution of quantum information over a quantum channel. In this paper, a rate-adaptive method is proposed by means of a channel coding scheme where specific low-density parity-check (LDPC) codes are adapted in the Slepian-Wolf coding system. Puncturing and shortening techniques are adopted to optimize their coding rates with all possible cases of error in QKD. This successful method utilizes the knowledge of the quantum bit error rate (QBER) based on the maximum-likelihood estimator with respect to the syndrome information. Its benefit is that avoids wasting sample keys in the traditional channel estimation and thus increases the size of the final secret key. Evidently, simulation results confirm an improvement in the reconciliation efficiency with minimal interaction that suitable for high QKD throughput applications.
Quantum Key Distribution (QKD) is a prominent solution to achieve proven secure data transmission between legitimate users despite any assumptions about the eavesdropper's computational power (given that the laws of quantum mechanics are correct). This remains true even under attacks by quantum computers. In recent years, there has been a great research interest in developing enhanced security constructions based on QKD. This is mainly driven by the envisioned threats of quantum computers to the traditional information security infrastructure based on public key cryptography. This research lies under the wide umbrella of the so-called post-quantum cryptography. However, for any QKD protocol, an accurate estimation of the Quantum Bit Error Rate (QBER) before the information reconciliation phase is crucial for both the efficiency and security perspectives. In spite of the importance of the QBER estimation step, the state-of-the-art literature still lacks a detailed investigation of the practical aspects of this issue. Therefore, this work aims to fill this research gap. An extension of the EnQuad simulator has been used to study the effect of QBER estimation on the efficiency and security of the BB84 QKD protocol for depolarizing quantum channels and individual Intercept/Resend Eve attacks. Various parameters affecting the QBER estimation process have been carefully investigated. Our evaluation has shown the significant importance of the QBER estimation step. Indeed, an empirical formula has been derived for calculating the required size of the sifted key subset (the so-called sharing rate) needed for the QBER estimation. This is a major contribution of the presented work.
Abstract Quantum key distribution (QKD) systems represent a cornerstone of secure quantum communication, relying on post-processing procedures to generate shared keys. Among these, error correction (EC) is a critical and computationally demanding step, where the estimation of the quantum bit error rate (QBER) plays a pivotal role in optimizing code rates for LDPC-based protocols. Traditional QBER estimation methods, grounded in physical models and statistics, often struggle with real-world variability and outliers, leading to suboptimal performance. In this study, we propose a novel machine learning framework for QBER forecasting, reframing the problem as a time-series prediction task. Leveraging real-world data from quantum transmitters, we evaluated a suite of models, including gradient boosting with autoregressive components, exponential smoothing hybrids, and deep neural networks, to predict QBER with greater precision. Through extensive experiments, our approach demonstrates significant improvements in error correction efficiency compared to traditional methods, particularly under challenging conditions like system calibration drifts and non-stationary signal behavior. The results highlight the potential of lightweight and interpretable machine learning models, such as gradient-boosted exponential smoothing, to outperform complex neural architectures in real-world scenarios. This research contributes to the advancement of quantum cryptography by enabling faster and more robust key generation, with reduced information disclosure during reconciliation. Our findings open new avenues for integrating machine learning into QKD systems for adaptive and scalable quantum communication.
Quantum cryptography provides methods for secret key distribution between the two distant users. An important step in quantum key distribution protocols is the correction of errors that occur during the transmission and implementation of the protocol. Here we consider error estimation and error correction with linear codes such as repetition code, Hamming code, low density parity check (LDPC) code. The paper investigates the increase in the efficiency of error correction using a combination of a repetition code and a LDPC code for a high error probability.
Quantum key distribution protocols (QKD) identify eavesdroppers on quantum channel based on laws of quantum mechanics. In the original BB84 protocol, unauthorized measurements on qubits are discovered after Alice and Bob sacrifice some random resulting key bits as a test and find out a mismatch rate. Decoy state protocol alerts photon number splitting attack when the decoy multiphoton pulses deliberately positioned by Alice are registered abnormally higher at Bob’s detectors than the single photon pulses are. E91 protocol is the first QKD protocol that ever brought about entangled atoms. Based on Bell’s theorem, a probability coefficient is constrained within a fixed range under the circumstances of interception. While in practice, bit error rate (BER) is not necessarily associated with vicious eavesdropping. Detection inefficiency, transmission loss, imperfect entanglement sources and many other factors contribute as false alarms. Error correction is an essential post-processing procedure to tolerate implementation limits, yet secure the accuracy of the transmitted key. Quantifying third party contaminations also helps setting an optimal BER threshold to decide if one should abandon all previous communications. In this work, we summarize major causes of bit error in various practical QKD protocols mentioned above and study whether error correction models, such as low-density parity-check code (LDPC), perform accordingly to different kinds of errors.