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arXiv:2408.00569

An Open-Source Library for Information Reconciliation in Continuous-Variable QKD

Cil, Erdem Eray, Laurent Schmalen

Published Aug 1, 2024• 2 citations
arXivHTMLPDF

Abstract

This paper presents an easy-to-use open-source software library for continuous-variable quantum key distribution (CV-QKD) systems. The library, written in C++, simplifies the crucial task of information reconciliation, ensuring that both communicating parties share the same secret key despite the noise. It offers a comprehensive set of tools, including modules for multidimensional reconciliation, error correction, and data integrity checks. Designed with user-friendliness in mind, the library hides the complexity of error correction, making it accessible even to users without knowledge of error-correcting codes.

DOI
10.48550/arxiv.2408.00569

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This paper presents an easy-to-use open-source software library for continuous-variable quantum key distribution (CV-QKD) systems. The library, written in C++, simplifies the crucial task of information reconciliation, ensuring that both communicating parties share the same secret key despite the noise. It offers a comprehensive set of tools, including modules for multidimensional reconciliation, error correction, and data integrity checks. Designed with user-friendliness in mind, the library hides the complexity of error correction, making it accessible even to users without knowledge of error-correcting codes.
Continuous-variable quantum key distribution (CV-QKD) requires highly efficient reconciliation techniques to operate at low signal-to-noise ratios and long distances. Multidimensional reconciliation addresses this challenge by transforming the physical Gaussian quantum channel into a virtual binary-input additive white Gaussian noise (BIAWGN) channel, enabling the use of modern errorcorrecting codes. In this work, we review the principles of multidimensional reconciliation, with a particular focus on high-dimensional constructions beyond the algebraic dimensions 1, 2, 4, 8. We describe the construction of the virtual channel, discuss practical coding schemes for reverse reconciliation, and analyse their integration with linear error-correcting codes. We also present an opensource simulation framework, HDirac, implementing multidimensional reconciliation for arbitrary dimensions, and use it to evaluate state-of-the-art LDPC codes. The results highlight key trade-offs between dimension, reconciliation efficiency, and frame error rate, providing practical guidance for CV-QKD system design.
Abstract Quantum key distribution (QKD) can provide information-theoretically secure keys for two parties of legitimate communication, and information reconciliation, as an indispensable component of QKD systems, can correct errors present in raw keys based on error-correcting codes. In this paper, we first describe the basic knowledge of information reconciliation and its impact on continuous variable QKD. Then we introduce the information schemes and the corresponding error correction codes employed. Next, we introduce the rate-compatible codes, the hardware acceleration of the reconciliation algorithm, the research progress of information reconciliation, and its application in continuous variable QKD. Finally, we discuss the future challenges and conclude.
Information reconciliation is an essential step of continuous-variable quantum key distribution (CV-QKD) because its efficiency affects both the maximum transmission distance and the final secret key rate of the whole system. Slice reconciliation can achieve high secret key rates for the CV-QKD systems under high signal-to-noise ratios (SNRs). However, it suffers from the high designing cost of the error-correcting codes in the multi-level coding and multi-stage decoding step. To reconcile one set of data with fixed SNR, multiple error-correcting codes with different code rates need to be designed. If the channel environment changed, the code rates need to change along to maintain high reconciliation efficiency, making it complicated and costly. In this paper, we introduce polar codes into slice reconciliation and proposed a scheme that is simply constructed, effectively performed, and well adapted to the systems with wide-range and variational SNRs. Simulation results show that the proposed scheme offers reconciliation efficiency over 95% for the systems with SNRs range from 1 to 10, which can support the systems with high secret key rates. The decrease of complexity and the increase of secret key rate have great significance for a practical CV-QKD system.
Quantum Key Distribution (QKD) is a communication method which exchanges secret keys using cryptographic protocols involving elements from quantum science. Continuous Variable (CV) QKD is a method to implement key exchange using sampling of Gaussian signals. Reconciliation in CV-QKD is fundamentally realized via coding of the Alice or Bob binary labels of the Gaussian samples using either one-way or interactive communications between the parties, Alice and Bob, over a public authenticated channel. We assume that the communication is performed through an Optical Wireless (OW) or Free Space Optics (FSO) channel. In that case the received signal suffers from stochastic fading due to pointing jitter or atmospheric turbulence. As a result of the channel fading and noise Alice and Bob Gaussian samples will not match. Information Reconciliation (IR) is the phase of the CV-QKD protocol that makes sure that Alice and Bob agree on a common and identical labeling of their samples, i.e. agree on a common stream of bits that we denote as “reconciled key.” The information reconciliation in CV-QKD could be done by one-way or two-way channel coding to correct the actual labels so that they do match. To do so Bob generates a sequence of parity bits using a systematic code. These bits are sent to Alice over an authenticated public channel. Alice then uses her own sequence of labels she obtains after quantization with the redundancy provided by Bob to recover Bob’s binary sequence. In this work we analyze the problem of information reconciliation for continuous variable quantum key distribution over a free space optics channel.
Information reconciliation is a crucial process in continuous-variable quantum key distribution(CV-QKD) systems. The slice error correction (SEC) reconciliation is appropriate for short-distance CV-QKD. However, the efficiency of SEC reconciliation schemes is significantly influenced by noisy channels with low signal-to-noise ratios (SNRs). In this paper, we present an enhanced information reconciliation scheme, termed AC-SEC reconciliation, which adds the new Gaussian sequences c with the original Gaussian sequences y before quantization in the SEC reconciliation to obtain secret key sequences with high variance and reduce noise interferences. Simulation results demonstrate that compared with the traditional SEC reconciliation, the proposed information reconciliation has lower frame error rate (FER) and higher reconciliation efficiency, which can increase the secret key rate (SKR).
Information reconciliation is a significant step for a continuous-variable quantum key distribution (CV-QKD) system. We propose a reconciliation method that allows two authorized parties to extract a consistent and secure binary key in a CV-QKD protocol, which is based on Gaussian-modulated coherent states and homodyne detection. This method named spherical reconciliation is based on spherical quantization and non-binary low-density parity-check (LDPC) codes. With the suitable signal-to-noise ratio (SNR) and code rate of non-binary LDPC codes, spherical reconciliation algorithm has a high efficiency and can extend the transmission distance of CV-QKD.