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IEICE Communications Express

Enhancing CV-QKD Information Reconciliation via Soft-Value Disclosure

Takumi Kamiya, Hiroyuki Endo, Eiji Okamoto

Published Mar 16, 2026• 0 citations
Publisher

Abstract

In continuous-variable quantum key distribution (CV-QKD) protocols, random bit sequences are encoded into quadrature amplitudes of weak coherent light. The homodyne measurement results of the quantum signals are continuous values that can enhance the error-correction efficiency through soft-decision (SD) decoding. However, implementing SD decoding in typical CV-QKD error-correction processes is challenging because the party receiving the quantum signal is not the same as the party performing the error correction. In this letter, we propose a novel method to overcome this limitation by sharing partial information on homodyne measurement results between two parties via an authenticated public channel, thereby enabling SD decoding. Numerical simulations demonstrated that the quantum bit error rate for error-free QKD transmission increased from approximately 1% using conventional methods to 3.5% using the proposed approach.

DOI
10.23919/comex.2025xbl0166

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In continuous-variable quantum key distribution (CV-QKD) protocols, random bit sequences are encoded into quadrature amplitudes of weak coherent light. The homodyne measurement results of the quantum signals are continuous values that can enhance the error-correction efficiency through soft-decision (SD) decoding. However, implementing SD decoding in typical CV-QKD error-correction processes is challenging because the party receiving the quantum signal is not the same as the party performing the error correction. In this letter, we propose a novel method to overcome this limitation by sharing partial information on homodyne measurement results between two parties via an authenticated public channel, thereby enabling SD decoding. Numerical simulations demonstrated that the quantum bit error rate for error-free QKD transmission increased from approximately 1% using conventional methods to 3.5% using the proposed approach.
The performance of the information reconciliation phase is crucial for quantum key distribution (QKD). Reverse reconciliation (RR) is typically preferred over direct reconciliation (DR) because it yields higher secure key rates. However, a significant challenge in continuous-variable (CV) QKD with discrete modulations (such as QAM) is that Alice lacks soft information about the symbol decisions made by Bob. This limitation restricts error correction to hard-decoding methods, with low reconciliation efficiency. This work introduces a reverse reconciliation softening (RRS) procedure designed for CV-QKD scenarios employing discrete modulations. This procedure generates a soft metric that Bob can share with Alice over a public channel, enabling her to perform soft-decoding error correction without disclosing any information to a potential eavesdropper. After detailing the RRS procedure, we investigate how the mutual information between Alice's and Bob's variables changes when the additional metric is shared. We show numerically that RRS improves the mutual information with respect to RR with hard decoding, practically achieving the same mutual information as DR with soft decoding. Finally, we test the proposed RRS for PAM-4 signalling with a rate 1/2 binary LDPC code and bit-wise decoding through numerical simulations, obtaining more than 1dB SNR improvement compared to hard-decoding RR.
A challenging issue in continuous-variable quantum key distribution (CV-QKD) is the improvement in error correction efficiency because random number bits are encoded in a quadrature of faint optical pulses. Herein, we propose an error-control information reconciliation method for CV-QKD based on our recently proposed fixed-bit polar code. In the present scheme, unreliable bits are embedded in the prepared “fixed bits,” enabling the detection and reproduction of errors in these bits without error correction, effectively improving the error-correction efficiency. Numerical simulations demonstrate that the efficiency of the proposed scheme is 10% higher than that of polar code-based reconciliation without fixed bits.
In continuous-variable quantum key distribution, information reconciliation is required to extract a shared secret key from correlated random variables obtained through the quantum channel. Reverse reconciliation (RR) is generally preferred, since the eavesdropper has less information about Bob’s measurements than about Alice’s transmitted symbols. When discrete modulation formats are employed, however, soft information is available only at Bob’s side, while Alice has access only to hard information (her transmitted sequence). This forces her to rely on hard-decision decoding to recover Bob’s key. In this work, we introduce a novel RR technique for PAM (and QAM) in which Bob discloses a carefully designed soft metric to help Alice recover Bob’s key, while leaking no additional information about the key to an eavesdropper. We assess the performance of the proposed technique in terms of the achievable secret key rate (SKR) and its bounds, showing that the achievable SKR closely approaches the upper bound, with a significant gain over hard-decision RR. Finally, we implement the scheme at the coded level using binary LDPC codes with belief-propagation decoding, assess its bit-error rate through numerical simulations, compare the observed gain with theoretical predictions from the achievable SKR, and discuss the residual gap.
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.
Continuous-variable quantum key distribution (CV-QKD) is a promising quantum-safe alternative to classical asymmetric cryptography that enables two authenticated parties to establish a shared secret over a potentially eavesdropped quantum channel. A key step in CV-QKD post-processing is information reconciliation, which leverages forward error correction (FEC) techniques to extract identical bit strings from noisy correlated data. In this work, we analyze the strict limitations on operating distance that are imposed by constant-rate FEC, severely limiting the practicability of CV-QKD systems in deployed optical networks. To overcome the distance limitations, we evaluate three strategies: (i) tuning modulation variance, (ii) adding controlled amounts of trusted detector loss, and (iii) the use of rate-adaptive FEC. All approaches are validated experimentally, compared in terms of performance, and we discuss implementation aspects. Our results show that while methods (i) and (ii) extend the operational distance of constant-rate FEC without the need for additional hardware components, they incur a significant penalty in secret key rate (SKR). In contrast, rate-adaptive FEC enables CV-QKD operation with performance close to the asymptotic SKR over a wide range of distances, provided that the reconciliation efficiency is chosen appropriately.
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).