New near-capacity continuous-variable quantum key distribution (CV-QKD) reconciliation schemes are proposed, where both the authenticated classical channel (ClC) and the quantum channel (QuC) for QKD are protected by separate forward error correction (FEC) coding schemes. More explicitly, all of the syndrome-based QKD reconciliation schemes found in literature rely on syndrome-based codes, such as low-density parity-check (LDPC) codes. Hence at the current state-of-the-art the channel codes that cannot use syndrome decoding such as the family of convolutional codes (CCs) and polar codes cannot be directly applied. Moreover, the ClC used for syndrome transmission in these schemes is generally assumed to be idealistically error-free, where the realistic additive white Gaussian noise (AWGN) and Rayleigh fading of the ClC have not been taken into account. To circumvent this limitation, a new codeword-based -rather than syndrome-based -QKD reconciliation scheme is proposed, where Alice sends an FEC-protected codeword to Bob through a ClC, while Bob sends a separate FEC protected codeword to Alice through a QuC. Upon decoding the codeword received from the other side, the final key is obtained by applying a simple modulo-2 operation to the local codeword and the decoded remote codeword. As a result, first of all, the proposed codeword-based QKD reconciliation system ensures protection of both the QuC and of the ClC. Secondly, the proposed system has a similar complexity at both sides, where both Alice and Bob have an FEC encoder and an FEC decoder. Thirdly, the proposed system makes QKD reconciliation compatible with a wide range of FEC schemes, including polar codes, CCs and irregular convolutional codes (IRCCs), where a near-capacity performance can be achieved for both the QuC and for the ClC. Our simulation results demonstrate that thanks to the proposed regime, the performance improvements of the QuC and of the ClC benefit each other, hence leading to an improved secret key rate (SKR) that inches closer to both the Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound and to the maximum achieveable rate bound.
New near-capacity continuous-variable quantum key distribution (CV-QKD) reconciliation schemes are proposed, where both the authenticated classical channel (ClC) and the quantum channel (QuC) for QKD are protected by separate forward error correction (FEC) coding schemes. More explicitly, all of the syndrome-based QKD reconciliation schemes found in literature rely on syndrome-based codes, such as low-density parity-check (LDPC) codes. Hence at the current state-of-the-art the channel codes that cannot use syndrome decoding such as the family of convolutional codes (CCs) and polar codes cannot be directly applied. Moreover, the ClC used for syndrome transmission in these schemes is generally assumed to be idealistically error-free, where the realistic additive white Gaussian noise (AWGN) and Rayleigh fading of the ClC have not been taken into account. To circumvent this limitation, a new codeword-based -rather than syndrome-based -QKD reconciliation scheme is proposed, where Alice sends an FEC-protected codeword to Bob through a ClC, while Bob sends a separate FEC protected codeword to Alice through a QuC. Upon decoding the codeword received from the other side, the final key is obtained by applying a simple modulo-2 operation to the local codeword and the decoded remote codeword. As a result, first of all, the proposed codeword-based QKD reconciliation system ensures protection of both the QuC and of the ClC. Secondly, the proposed system has a similar complexity at both sides, where both Alice and Bob have an FEC encoder and an FEC decoder. Thirdly, the proposed system makes QKD reconciliation compatible with a wide range of FEC schemes, including polar codes, CCs and irregular convolutional codes (IRCCs), where a near-capacity performance can be achieved for both the QuC and for the ClC. Our simulation results demonstrate that thanks to the proposed regime, the performance improvements of the QuC and of the ClC benefit each other, hence leading to an improved secret key rate (SKR) that inches closer to both the Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound and to the maximum achieveable rate bound.
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.
Continuous-variable quantum key distribution (CV-QKD) offers an attractive route to information-theoretic secure communications using coherent detection and largely off-the-shelf telecommunication components. However, practical deployment remains constrained by the efficiency and reliability of information reconciliation in the low signal-to-noise ratio (SNR) regime, finite block-length effects, and the need to operate robustly under time-varying channels. This thesis addresses these challenges by developing short-block polar-coded reconciliation schemes, an adaptive incremental-redundancy hybrid automatic repeat request (IR-HARQ) framework tailored to CV-QKD, and a simultaneous quantum and classical communication (SQCC) architecture with joint classical--quantum optimization. Firstly, this thesis investigates polar codes as a finite-length alternative to conventional LDPC-based reconciliation. By constructing and evaluating a series of progressively enhanced reconciliation architectures, it is shown that short-block polar codes can provide improved block-error-rate (BLER) performance and higher reconciliation efficiency in the operating regime relevant to practical CV-QKD systems. The study further analyzes implementation trade-offs, including computational load distribution between Alice and Bob and the impact of decoder choices, identifying list decoding with moderate list sizes as an effective performance--complexity compromise. Secondly, to address channel variability and the sensitivity of fixed-rate reconciliation at low SNR, an IR-HARQ reconciliation protocol is proposed. Instead of committing to a single code rate, the protocol progressively reveals additional redundancy across retransmissions, effectively lowering the coding rate only when needed. A reliability-driven frozen-bit scheduling strategy is developed to maximize the error-correction benefit per disclosed bit under finite-length constraints, while ensuring that the resulting leakage is properly accounted for in privacy amplification. The proposed IR-HARQ design significantly improves reconciliation robustness and extends the achievable secure distance compared with one-shot fixed-rate baselines. Thirdly, this thesis considers SQCC, where classical data transmission and CV-QKD share the same physical link. A power-allocation model is established through the power ratio between the quantum and classical components, and the resulting classical and quantum error behaviors are characterized. By incorporating successive interference cancellation and forward error correction on both components, the proposed SQCC designs enable simultaneous classical throughput and secure key generation with controllable trade-offs among reliability, excess noise, and secret key rate. Overall, the thesis demonstrates that short-block polar coding, when combined with adaptive IR-HARQ and SQCC-aware receiver processing, provides a coherent framework for improving the practicality of CV-QKD under finite-length and time-varying conditions, thereby supporting more resource-efficient and deployable quantum-secured communication systems.
This technical report proposes a unified error correction and reconciliation framework designed specifically for improving the secure key rate of Quantum Key Distribution (QKD) protocols, particularly in Continuous-Variable (CV-QKD) systems. Problem Addressed: Existing QKD reconciliation methods rely on standard binary codes, which fail to leverage the inherent geometry of the lattice channels used in CV-QKD. This leads to reduced efficiency, especially when the signal quality is low (low SNR). Key Innovations: Lattice-Native Coding: The design employs Low-Density Parity-Check (LDPC) codes defined natively over integer rings (Z-sub-q), allowing direct alignment with the geometric structure of the quantum channel. Geometry-Preserving Interleaving: A novel, low-discrepancy interleaver is introduced to optimize error spreading while maintaining local geometric structure during encoding and decoding. Leak-Aware Reconciliation Ledger: A dynamic ledger is used to precisely track all information leakage (syndrome sum) during the error correction process. This tracked leakage directly sets the length for Privacy Amplification, ensuring rigorous and composable finite-key security bounds.
Continuous-variable quantum key distribution (CV-QKD) is a promising technique of supporting quantum-safe wireless networks in the emerging 6G era, mapping quantum information onto the amplitude or phase of electromagnetic waves. However, conventional CV-QKD reconciliation methods often assume ideal classical side-information channels, which is an unrealistic scenario in practical deployments. To address this critical challenge, we propose a novel protection scheme integrating Polar and low-density parity-check (LDPC) codes. Specifically, Polar codes safeguard quantum transmissions due to their superior performance for short block lengths, while LDPC codes robustly protect the classical side information exchanged over auxiliary classical channels. We further enhance the CV-QKD performance by harnessing a soft-decision Polar decoding method combined with protocols specifically tailored for reverse reconciliation (RR) and direct reconciliation (DR). In the RR scheme, conceived decoding complexity is strategically distributed: Polar decoding is performed by Alice, and LDPC decoding by Bob, hence significantly reducing the computational demands compared to traditional schemes where both decoding processes are invoked at a single node. Simulation results validate the effectiveness of our approach, demonstrating that Polar codes consistently outperform LDPC codes in quantum transmission scenarios having short block lengths under 512 bits. These findings emphasize the strong potential of Polar coding-assisted CV-QKD in achieving secure and efficient quantum-safe control information transmissions, paving the way for practical implementation in next-generation wireless networks.
Quantum key distribution (QKD) provides information-theoretic security by leveraging quantum mechanical principles, while Terahertz (THz) communications offer unprecedented data rates for next-generation networks. We sketch out an evolutionary pathway for bridging these domains by critically appraising THz-based continuous-variable QKD (CV-QKD) systems conceived for wireless environments like space-air-ground integrated networks (SAGINs) and vehicle-to-everything (V2X) scenarios, where time-varying frequency-selective fading poses critical challenges. To address these issues, we elaborate on the feasibility of THz based CV-QKD applications from a wireless perspective. Specifically, we commence by highlighting a typical CV-QKD protocol. Then present three sophisticated CV-QKD system designs.Firstly, we propose a codeword-based – rather than syndrome-based – reconciliation scheme capable of accommodating diverse forward error correction (FEC) codes, imposing a similar complexity on the transmitter and receiver. As a further improvement, we demonstrate that powerful irregular convolutional codes (IRCCs) attain a near-capacity performance, thus offering longer secure distance and/or improved secret key rate (SKR).Secondly, the secure boundaries derived for the optical and THz band – even down to microwave frequencies – demonstrate the feasibility of short-distance THz CV-QKD systems. Furthermore, multiple-input multiple-output (MIMO) schemes are harnessed for improving the SKR performance.Thirdly, an orthogonal time frequency space (OTFS) modem-based CV-QKD system is conceived for time-varying frequency-selective THz fading channels. Finally, we conclude by identifying several promising research directions for CV-QKD systems.
Reconciliation is a necessary step in postprocessing of continuous-variable quantum key distribution (CV-QKD) system. We use globally coupled low-density parity-check (GC-LDPC) codes in reconciliation to extract a precise secret key from the raw keys over the authenticated classical public channel between two users. GC-LDPC codes have excellent performance over both the additive Gaussian white noise and binary-erasure channels. The reconciliation based on GC-LDPC codes can improve the reconciliation efficiency to 95.42% and reduce the frame error rate to 3.25 × 10–3. Using distillation, the decoding speed can achieve 23.8 Mbits/s and decrease the cost of memory. Given decoding speed and low memory usage, this makes the proposed reconciliation method viable approach for high-speed CV-QKD system.